SQT

is this an example?

A_1={a,b}
A_2={b,c}
A_3={c,d}
I={1,2,3}
J={1,2}

then left hand side is {b}
right hand side is empty
so no inclusion

>>9039062
thanks, I was just being dumb

>>9039057

>>9039062


So as soon as you add another set to your indeces, you introduce the possibility of it being disjoint with one of the others?

Just took a calculus I class and physics I class (algebra). I didn't really "understand" physics I and just plugged and chugged which got me a 90. I want to relearn physics I but with calculus. what's a good book and video series?
I found this: https://www.youtube.com/watch?v=oBb3ZjVpmXs&list=PLA7857619F91267C0 but there's no electricity and magnetism

>>9039758
Dunno man, just go to Kahn Academy or something. It seems like a waste to get a book just to remember basic physics. Then get a book on something you want to photos on, Landau has them all, but I don't like his notation.

>>9040480
Phocus*

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so my education on maths more or less ended with linear algebra in secondary school, and now im trying to get to grips with calculus on my own. can someone please explain to me what the fuck the rules are for variable naming in calculus? because my understanding of things is generally that ab=a*b, and yet i see ab being used as a single variable name in calculus.

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What did he mean by this

What is the best way to find top professors in a given field of study? Google scholar? Researchgate? In EE and specifically photonics/optics, RF/Electromagnetics, image processing/DSP fields

>>9040480
preferably I would just download the book.

>>9040546
can one of you mongs answer this pleaseee? Have asked it for the past 4 sqt

>>9040547
You should probably get Calc 3 before taking a physics book. Before that, review physics with your high school book or online vids.

>>9039057

J is a subset of I, so you perform fewer intersections and end up with a set that's always at least as big as the intersection over I

>>9040691

more generally if J and I are countable, the cardinality of the intersection of a sequence of sets is a decreasing monotone function.

How do I learn about organic chemistry of pharmacology to better understand amphetamines?

Any books or resources for thos without a background in chem?

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>>9039057
I have an inequality here in pic related. Perhaps someone could help me with it?

It is from a problem set and the problem below and above it are pretty easy, so I assume this problem isn't too hard but I just don't see an opening. I have no idea with how to start.

Making a webapp just for shits that generates primes. I implemented the sieves of eratosthenes, sundaram, and atkins. Any other ones, or ideas of other shit I should put in? I'm thinking a graphing utility to time them would be neato

>>9041694

Maybe write the numbers as

A =Σαk*10^k, B=Σβk*10^k
Where αk, βk are their digits

Seems useful but unsure where to go from there...

>>9041841
Yeah, that's the obvious start (I think). But after that I see no identity to apply.

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How does the eletrons of a current pass through the battery if a battery is basically just two eletrically polarized compartments which are separated from each other?

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I am smart enough to take a dual major in Physics and Math in just 4 years, but I want to get into the tech industry, because one day I want to work in Japan and IT is the only way in if I don't want to become an eigo-sensei. The Japanese are extremely conservative when it comes to work shit, they look solely for CS undergrads for jobs in software engineering and that kind of stuff. What does /sci/ think I should do? I want to be proud of myself and study cool stuff, but I also want to move to Japan. Maybe a CS degree with dual minors in Math and Physics?

Could I become a climate scientist via online courses (with certifications and whatnot)? There's a lot of official stuff online that offers certifications from accredited universities and colleges. I can't afford to go to college and this is way more affordable.

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Why the voltage of a circuit isn't equal in all parts of the circuit just like how the hydraulic pressure is in a pipework circuit?

Why does the eletric pressure of a current drop after each resistor in the circuit?

>>9040543
when you say [math]ab[/math], do you mean [math]\text{d}x[/math]? Because [math]\text{d}x[/math] is an infinitesimal change in [math]x[/math], and can be manipulated as a single variable. Otherwise your book is pulling some retarded shit that I've never seen elsewhere.

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>>9041951
pic related, dt and dx. dt and ds are defined as scalars here, i just dont quite get the rules in order to make complete sense of this expression.

>>9041962
This is shitty notation. Get some other book.

>>9041973
what book should i read? i have a poor grasp on math, but i see this notation being used to describe derivatives all the time

>>9041975
I've no idea since my background is pure math. Why are you studying calculus after all?

I began calculus with Apostol, you should try it to see if you can manage. Spivak is also good. Neither will pull shit like this, if the author doesn't even define expressions properly just throw the book in the trash, calculus is already "hard" as far as baby math goes.

>>9041977
to better get to grips with neural nets, which require i understand derivatives

Where, exactly, does one find interesting, juicy mathematics problems to sink their teeth into? A good textbook will obviously have some. Anywhere else?

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>>9041896
Please help

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I was checking my answers for calc in wolfram and one answer was wildly off. Eventually I figured out it's because wolfram and I disagree on the derivative of sin(x + pi/3)
All of my knowledge says it should just be cos(x + pi/3), but picrelated is what wolfram is saying.
I'm sure as hell not going to pay them just to understand this answer, so can anyone explain what's going on?

>>9041962
What a strange notation. It looks to me like you're dealing with the formal definition of a derivative, and the notation is usually (f(x+h) - f(x))/h, at least in my experience.

>>9042557
I'm doing a Dual Degree in Mathematics and Computer Science, and going to finish a year early. You could do the same but push a physics minor in there to make it 4 years

>>9042557
Having finished your BSc you may apply for masters in Japan. I just want to warn you that one may find software engineering overly boring.

>>9041917
https://en.wikipedia.org/wiki/Hydraulic_analogy
Answer: you're wrong about hydraulics, there are
pressure differences across obstructions in pipes.

>>9042568
pretty much, i just need a good explanation that works for someone whos really rusty on their maths

I'm learning formal logic, for some reason the following doesn't seem correct:

"Rewrite the statement:
Everybody trusts somebody in formal language. "

Let, X = people, and
Y = a person
P(x, y) = ∀ x, ∃ y such that x trusts y.

This just doesn't seem as formal as the examples in my text.

Let P(x) be the predicate “-10 < x < 10” with domain Z (set of all positive integers. Find the truth set of p(x).

=

{-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Or is it not inclusive of 0?

>>9039057
Is math related to science? If so, how so?

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How do I stop being a brainlet?

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What's the name of this function?

>>9042918
Grosine

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Is time a requirement for 3d objects to move through space or does the movement of 3d objects create time?

>>9043137
Spacetime is one. So yes

>>9042819
X should be a person as well

Statistics question. I have a data set that seems to follow a normal distribution. I want to find out if there are anomalies (dont know the word for this, reproducible outliers?), but I also want to be able to reason about this myself. Are there any recommended online courses (Ive a CS masters but little training in statistics) that'll get me to the level of being able to do this in a reasonable timespan?

>>9043229
Or a book I could learn.

>>9043229
>reproducible outliers

Outliers only make sense in the context of a sample, not the actual distribution. If you're looking for outliers in a sample from a normal distribution, use Grubb's test.

>>9043248
What if you have a graph that looks like the bell curve but with a narrow 2nd top somewhere that is reproducible in new data sets? Is there a word for that?

>>9042805
Basically, h (or dt in this case) is the Δx of when you're figuring out a secant line. You take the limit as Δx approaches 0, thus getting the slope of the tangent line.
The formal definition of a derivative is really just taking the slope of the line that you're generating there.
It's basically the old rise/run to find slope that you would use in early algebra. You can think of it as
x = x1; x+h = x2
f(x) = y1; f(x+h) = y2;
Which makes the formula into (y2 - y1)/(x2 - x1) but obviously x2 is x+h, so x+h-x is just h.

Is this helping? I don't really know if I'm making sense, I'm kind of tired.

>>9043353
m8 i have no fucking clue about half of what you said, my maths education ended at 16 and that was 7 years ago now

>>9040546
in any university?
Ivy League

>>9043229
I reccomend you learn R
>r-tutor.com
give all the distributions a read
keep in mind this is only for a quick start, I highly reccommend a book

for book, I like Ross (libgen)

>>9039057
not true in general since one might have J = I

>>9039057
Will
calculus 1
Intro to Chem (toughest expert on campus, but also took this in high school pretty much)
And cop2000 ( intro to programming)
With a 30 hour/week job be detrimental to my learning and success ?

I did just have the first two but through on the cop2000

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Do any chess engines take either
>game time remaining
>previous moves (in particular blunders)
into account?

How do population dynamics work?

I want to estimate the Jewish population in 2017 supposing the Holocaust never happened

https://en.wikipedia.org/wiki/Jewish_population_by_country
>In 1939, the core Jewish population reached its historical peak of 17 million
>Due to the Holocaust, the number was reduced to 11 million in 1945.
>The world's core Jewish population was estimated at 14.31 million (around 70% of the world's "enlarged" Jewish population) in early 2015.

I asked a 19 year old girl if she had sex before and she said her body "isn't ready" for sex (probably relevant: she's extremely skinny). What did she mean by this?

>>9044095
It means she doesn't want to fuck you.

>>9043570
So any professor at a high ranking EE school should be top tier? Just wondering because I am applying to top 5,10 schools for grad school and have also been told that a top professor matters more. Just wondering if I could find like maybe top 20,40 schools that have a really good professor as a safety school.

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Have some pharmaceuticals done more harm than good (thinking of fentanyl)?

>>9044239
Sure, lots of them. Most recreational drugs are also prescription medicines. And many medicines have ended up being withdrawn (or at least restricted) after the side effects became better known (e.g. Thalidomide).

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How do I make the filesize of a 100x100 jaypeg file as large as possible?

Is it possible to re-learn math and physics within a month and a half?
what would it take to do so?
not necessarily 100%

>>9044924
So that it wont compress easily, lots of different colors, lots oft irregular patterns

>>9045621
Is it possible to add metadata to a jpg? If so, that'd be another thing one could try to abuse.

>>9042564
cos(x+π/3)-sin(1/6(π-6x))=0

When do I know whether the uncertainty is greater or equal to either the reduced planck constant or the reduced planck constant over 2

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How do i answer question 1?

I'm starting my first semester of college in about a month, taking linear algebra. I have a TI-84 I used in high school calculus. Is there any reason I'd want a newer calculator, either new features or just increased efficiency? Or is the calculator not all that relevant?

>>9046089
X=0 Y=20
A square will be bigger than simple addition

>>9046348
Don't bother wasting money if you already have one, they have all the same features but just look more fancy with all those colours

>>9046348
I mean, the CX-CAS can do algebra and calculus for you. So you could get that if your professors would be okay with you using it.
Plus, it also intelligently automatically fills in parenthesis, which is a godsend.

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>>9046348
>using a calculator

Is it actually possible to definitively crack one of the CIA numbers stations without one of their pre-shared keys? Like could you get to the point where you have a solution and know for a fact that it is the right message?

>>9042887
>set of all positive integers
so I'd say it doesn't include 0, and it also doesn't include the negatives. so just 1 thru 9

>>9043389
Think about a straight line.
It has the form
y = mx + b where m is the slope and b is the y intercept. On a line, it is easy to see what the slope is. It is m, as just stated. Furthermore, the slope is the same no matter what point you test it at.

Now consider a function like
y = x^2
In some places, the slope is negative. In other places, it is positive, and at one point in particular, the slope is 0.

In this case, the slope is not constant, like it is with the line, but instead varies throughout the function. All development of calculus studies how the slope of a function is related to the function. Instead of getting a number, you usually get another function.

Going back to our examples, in calculus the slope is defined as dy/dx. You might also see it written as y' or y with a dot over it. They all mean the same thing.

You don't have to worry about the definition of an integral or derivative until you get to analysis, as all previous explanations such as your text and this post are extreme simplifications. But unless you study pure math or need to write a program that does calculus for you, it doesn't matter. So just learn the rules for derivatives and integrals.

For a line, dy/dx = m if you follow the rules, which is what everyone learns in grades cool without knowing calculus.

For the parabola, dy/dx = 2x. When x is negative, the slope is too. When x is 0 the slope is 0. When x is positive, so is the slope. Look at a graph of a parabola and it is apparent.

Finally, an integral is essentially the inverse of a derivative. Just like adding/subtracting or multiply/divide or exponents and logarithms. Again, this is very basic and 99% of stem majors don't even know why they do it, so don't sweat it. Just learn the techniques.

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I'm on chapter 3 of this and so far have been having trouble solving most of the proof exercises on my own, giving each at most 30 minutes before giving in if I can't figure it out (assuming that's about what the author expects of the average reader).

Should I just give up on the thought of any STEM degree that isn't plug and chug? I just wanted the math education that I never had before starting college, not these feelings of worthlessness.

What's the best way to learn multiplication tables?

I skipped 3th-5th grade due to moving a new country with a foreign language (fuck off /pol/, it was a white first world country to another white first world country, seriously fuck off) and so the moment I got back into school calculators were already in use.

Retard here.

Can a change be physical and chemical at the same time? In other words, what does the term ''Physical-chemical change'' actually imply?

Is an explosion a physical or chemical change? (ex. the exploding of nitroglycerine)
Help is appreciated.

Resolution Logic

I have 3 claims.
C1 = { ~S(x), ~SCIS(x), CS(x), IT(x) }
C2 = { ~S(a), ~SCIS(a), ~CS(a) }
C3 = { ~S(a), ~SCIS(a), ~IT(a) }

There's no way to find the empty clause is there...? (i.e. the following argument is false)

I got the clauses by the argument:
“Every student in the SCIS is a CS student or an IT student.
Therefore there is a student in the SCIS being a CS student or an IT student”

I did formalization, skolemization, negated the conclusion, and then got the clauses I got. I don't see anyway to reach an empty clause by resolution. Did I get the correct conclusion?

>>9047409
As a kid I used flashcards. 12x12 times table is a good standard. Learn 1 row, then add another row to the deck and continue. You find patterns and tricks as well. Like for 9s theres a fingers trick you can google to learn. You also eventually get faster at just adding a number over and over in your head to find the solution once you know the basic multiples.

>>9047389
Proofs are hard at the beginning, just keep at it.

>>9047409
>>9047443
Consider reciting them out loud like "7, 14, 21..." but also as "1 times 7 is 7, 2 times 7 is 14, ..." That's what I was required to do in school.
It's an easy skill to practice since you can do it while walking, sitting, driving, etc.

Will smoking weed permanently hinder my /sci/ abilities? If so, how often can I get away with it without worrying?

>>9047523
Yes. 0 times.
If you care about your brain don't take substances who heavily interact with your brain.

Propositional Logic/First Order Logic

“Every student in the SCIS is a CS student or an IT student.
Therefore there is a student in the SCIS being a CS student or an IT student”

S(x): x is a student;
SCIS(x): x is in SCIS;
CS(x): x is CS student;
IT(x): x is an IT student

1st sentence:
Ax( S(x) <and> SCIS(x) --> CS(x) <or> IT(x) )

2nd sentence:
Ex( S(x) <and> SCIS(x) <and> (CS(x) <or> IT(x)) )

Is this correct?

Can I just use integration rules instead of Riemann sums? I'm working through a calc book and this chapter wants to integrate using Riemann sums. Seems kinda of pointless since no one uses it anymore

>>9048089
Your sentence is essentially of the form [math]\forall x \phi \implies \exists x \phi[/math], which follows from universal instantiation + existential generalization, [math]assuming that the domain of discourse is nonempty[/math].

Otherwise, you couldn't rule out the possibility that there are no students in the SCIS at all, in which case the premise
>“Every student in the SCIS is a CS student or an IT student.
would be vacuously true but the conclusion would be false (since no students exist).

Though once you grant that assumption of existence, the logic becomes valid and everything else you've written is correct.
(That said, you seem to have a predicate SCIS(x) so I'm not sure what exactly your domain of discourse is.)

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Suppose a regular tetrahedron is inscribed in a sphere. Now suppose a line is drawn connecting any two points in the shortest distance possible around the surface of tge sphere. What percentage of the circumference of the sphere would this line be?

>>9047389
>expecting math to be easy
You gotta let go of some of your pride, kiddo.

>>9047417
Everything is physical. :^)

>>9048795
one third

1) How do I reduce 5 * (2^n ) + 3 * (2^n) - 5 -- the solution has 2^n+3 - 5 but I don't remember the algebra rules to reduce it to this.

2) Does [Sum k=1 to n-1 2^k ] = (2^n - 1)/(2-1)? It looks like it does based off a few examples I've seen.

>>9049340
>How do I reduce 5 * (2^n ) + 3 * (2^n) - 5
a*b^n+c*b^n
= (a+c)b^n

> Does [Sum k=1 to n-1 2^k ] = (2^n - 1)/(2-1)
https://en.wikipedia.org/wiki/Geometric_series

>>9049351
Thanks on 1)

It still isn't clear if my generalzation is correct on 2)

I know sum k=0 to n a^k = a^n+1 - 1/ a- 1

but is [Sum k=1 to n-1 2^k ] = (2^n - 1)/(2-1) correct? A recurrence relation proof I am doing relies on this guess of mine.

>>9049351
Also,

5 * (2^n ) + 3 * (2^n) - 5 = 2^3 * 2^n = 2^n(n+3) - 4 is that what happens?

>>9049361

2^3 * 2^n - 5 = 2^(n+3) - 5 ******

>>9049357
>but is [Sum k=1 to n-1 2^k ] = (2^n - 1)/(2-1) correct?
if
sum k=0 to n a^k = (a^(n+1) - 1)/ (a- 1)
then
sum k=0 to n 2^k = (2^(n+1) - 1)/ (2- 1)

and so
sum k=1 to n-1 2^k
=(sum k=0 to n-1 2^k) - 2^0
=(sum k=0 to n-1 2^k) - 1
= (2^n- 1)/ (2- 1) - 1

>>9049364
yes

>>9049369
I am still unclear on this.

Here is my problem

Problem:

a*_n_* = 2a*_n-1_* + 5, a*_0_* = 3

I noticed this follows the pattern:

2^n (a*_n-n_* ) + 2^n-1 (5) + 2^n-2 (5) + ... + 2^1 (5)

= 2^n (3) + 2^n-1 (5) + 2^n-2 (5) + ... + 2^1 (5)

Now here us what I am focused on:

2^n-1 (5) + 2^n-2 (5) + ... + 2^1 (5)

I think this is:

[Sum k=1 to n-1 2^k ] = (2^n - 1)/(2-1)

which becomes the below,

2^n (3) + 5 * (2^n - 1)/(2-1)

= 3(2^n ) + 5 * (2^n - 1)/(1)

= 3(2^n ) + 5 * (2^n - 1)


Is there something wrong with this summation?

>>9049377
>I think this is:
>[Sum k=1 to n-1 2^k ] = (2^n - 1)/(2-1)
>Is there something wrong with this summation?
yes, for example if n=2 then
[Sum k=1 to 2-1 2^k ]
=[Sum k=1 to 1 2^k ]
= 2^1
=2

(2^2 - 1)/(2-1)
=(4-1)
=3

see
>>9049369

>>9049380
= (2^n- 1)/ (2- 1) - 1

= (2^n - 1)/0

That doesn't make any sense to me.

What summation pattern does the 2^n's follow in this pattern then?

2^n-1 (5) + 2^n-2 (5) + ... + 2^1 (5)


Somehow I got the right answer, but apparently for the wrong reason!

>>9049391
>That doesn't make any sense to me.
its
[(2^n- 1)/ (2- 1)] - 1
=[(2^n- 1)/1] - 1
=(2^n-1)-1
=2^n-2

>>9049393
Maybe I am doing it wrong.


If you get the recurrence relation to the pattern:

= 2^n (3) + 2^n-1 (5) + 2^n-2 (5) + ... + 2^1 (5)

and just focus on the

2^n-1 + 2^n-2 + ... + 2^1

part

then what pattern would you say the

2^n-1 + 2^n-2 + ... + 2^1

follows summation wise?

somehow I am getting the right answer for the wrong reason. I want to know the correct summation for this

I think it's [sum k=1 to n-1 2^k]

>>9049408
>2^n-1 + 2^n-2 + ... + 2^1
yes this is
[sum k=1 to n-1 2^k] = 2^n-2

>>9049415
okay so the math comes out to

2^n (3) + 5 * 2^n-2

= 3(2^n) + 5(2^n-2)

= 2^3(2^n)

=2^(n+3)

But the answer in the book says the answer os

2^(n+3) - 5.

What did I do wrong here?

>>9049431
i just realized that math is all wrong. im fucking confused. i somehow did incorrect steps and got the answer right. this isn't for homework, but for my own understanding.

>>9049437

The problem is

a_n = 2a_n-1 + 5, a0=3

Ans: a_n = 3*2^n + 5(2^n-1) = 2^n+3 - 5

it looks like its saying the sum is (2^n-1) instead of 2^n-2

>>9049415

is my book wrong? Should >>9049446

be

3*2^n + 5(2^n - 2) instead?

>>9049475
bump on this.

If I'm floating in the air because magic, and I stick a fork into an outlet, will I be shocked?

>>9049666
While I'm at it, why would you die in a bath tub that has electricity running through the water?

Why would the electric run through you when the water has way less resistance

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Scientifically and ethically speaking, given the massive advanced in STEM over the past thousand years, should eugenics programs be implemented to prevent too many undesirable traits like allergies and bad eyesight from being in the gene pool?

>>9049702
Bad idea, literally diversity is strength

Sup /sci/

Something clicked inside me and now im super into math, i was actually thinking about changing my degree to physics but i think its a waste 3 years into my engineering degree, still i find it deeply interesting to learn new math stuff,

And good books or topics for entry-level big-boys-math?

I tried watching a series on tensor calculus but i find it abstract as fuck, is complex analysis or differential geometry any more simple to represent or to get cool tricks out of it?

Im currently into control theory, (Fourier, Laplace and shit), PDE's and hydrodynamics, so nothing terribly far from this would be ideal,

Also, any good books on quantum mechanics for absolute retards out there? I was very excited about that when i was learning about Fourier transformations

>>9049770
>not having invented calculus yourself at the age of 5
Congratulations, you're literally retarded.

Specific Question:
Can functions return sets?


Reason for question:
g(n) ∈O(f(n)) ∃ k,L : ∀n > L, g(n) < k⋅f(n)

This is the definition of big O notation.
Looking at the first part, to say that g(n) is an element of O(f(n)) would imply that the latter returns a set of functions with the growth rate of f(n) right?

>>9049792
big O notation is just an unintuitive use of the 'element of' symbol

f and g are just your usual functions with numbers as ouput

>>9049797
Okay, so it's just the notation?

Could you answer my first question? Can mathematical functions return sets or any type of result?

>>9049800
>Can mathematical functions return sets or any type of result?
yes

consider f(n)={n}

>>9049802
Okay cool, just never encountered it in HS math.

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If the Universe's expansion is constantly accelerating, how come gravity keeps things together just the way they are at least on a local cluster level? I mean, the distance between the Moon and the Earth is constantly getting larger, is it not? What am I missing?

>>9044120
But can you prove that mathematically?

around 3 months ago, everyday, iirc there was this anon making a list full of math books aimed for those wanting to do a "math minor", he even created a thread about this list and kept improving it
did someone screenshot this list? can I have it?

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What exactly is "Analysis" in mathematics? Wikipedia says it deals with limits, differentiation, and integration, but isn't that just calculus?

Also what does pic related mean?

>>9044924
>>9045621
This. Use some random noise gen

>>9047012
thats not what i need to know m8. i need to understand what a derivative is and how it works, so i can write a backpropagation algorithm and actually understand it.

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Is problem solving major method of learning math? How much will I loose if I will just read math books without doing problems?

>>9050260
try watching this

https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

How do I determine the smallest fixed point of a functional?

>>9041694
what the fuck does "half of their digits on the sinistral side" even mean

non-native english speaker here

>>9050165
>isn't that just calculus?
Yes.

How do you write the dirichlet generating function for the sequence ln(n) in terms of the riemenn zeta function?

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which is more aesthetic
which is more practical

[math]-x+a[/math]
or
[math]a-x[/math]

[spoiler] [math]\forall a \in \mathbb{C} [/math] [/spoiler]

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If I use a voltmeter on a neutral medium (i.e. earth) and the last portion of a circuit, right before the battery's negative end like in pic related, am I going to get a 0 tension reading?

>>9050573
a-x obviously

>>9050573
But [math] \C [/math] isn't commutative, so you have to use [math] \R [/math]

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1. Is pic related decent?
2. Does this structure have a name? It's defined as [math](S,\,\mathord\to,\,\bot)[/math], where S is a set, → is a binary relation and ⊥ an element of S, such that [math]\forall s\in S,\,s\ne\bot\quad \bot\to^+s[/math] where →+ is the transitive closure of →. It's basically a pointed graph.

>>9050626
>1. Is pic related decent?
why don't you read it and find out?

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Am I a brainlet or does this "proof" not flow at all.

His only lead up to this is the definition of a derivative from first principles:

[eqn]f'(x) = \lim_{\delta x \to 0} \frac{f(x + \delta x) - f(x)}{\delta x}[/eqn]

and he defines a function [math]f[/math] to be continuous at [math]x = a[/math] if:

[eqn]\lim_{x \to a_-} f(x) = f(a) = \lim_{x \to a_+} f(x) = \lim_{x \to a} f(x)[/eqn]

>>9050677

It may just be bollocks.

This is a really basic beginners textbook. I'm already familiar with all these topics from a physics perspective so they should be easy.

However the book has 5 reviews on Amazon, 3 are scathing, and 1 is by the author. So it may just be an absolutely shit book.

(my coworker was throwing out textbooks and I saved it from the trash, maybe it should go back there)

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>>9050594
pls

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Suppose there is

y = x - sin(x),

where x is in radians and y is a known constant, is there a general solution like

x = ?

Is it even possible to obtain a (closed form?) solution like that or does one have to use numerical methods?

>>9050552
Apparently I accidentally walked into the stupid answers thread.

>>9050796
In my language we don't even have the word "calculus", we only say "analysis".
If the English language has both words, there must be a difference between them, but I assume that one is just a subset of the other.
So maybe calculus is a subset of analysis or something.

>>9050165

It's a specific equation that is interesting because it is extremely sensitive to error yet tends to form that shape.

It is defined in terms of rates of change of x y and z

To calculate it, you start a given point and calculate these rates of change. Then you move this point proportionally according to these rates. Then you calculate the rates of change again.

You can never calculate your point's position to infinitely many decimal places. Thus the error from the last calculation is used in the next one. Two points that start close to each other end up far away.

>>9050842
All I know is that most universities offer analysis as one of the last super-advanced math classes. You're done with multivariable calculus by the second year, maybe the first if you're good.

>>9050842
I mean I hate to quote Wikipedia but
https://en.wikipedia.org/wiki/Mathematical_analysis
>Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis.

Is there a wavelength where a focused EM beam can be used to transmit data without it being detectable for anyone not close to the receiver within the atmosphere?

>>9041694
>>9050518
"sinistral" is a pretentious SAT word that means "left hand" but I have no idea what the fuck that condition requires specifically.

I assume that for A = 42195611, B = 42110912 meets the criteria, or if B=12197878 that would also meet the criteria. But what about for natural numbers with an odd number of digits? Does the "sinistral side" include the "center" digit? Does "more than half" mean strictly more?

how to make regression to a relation with one input multiple outputs?

>>9049981
Assume that she did want to fuck you. Then she would have fucked you right then and there, no matter whether her body was "ready for sex" or not. This contradicts the fact that she did not fuck you. Therefore she does not want to fuck you. Q. E. D. Filled-in square.

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Hey guys which EE specialization between the following has the best job outlook for national lab work or industry R&D:
-Photonics
-Applied Electromagnetics
-RF/millimeter wave circuits
-Analog circuits
I like all of the options but can't find much info on which is the best path towards my goal

>>9051323
>Photonics
That one sounds the coolest so go with that.

This is how I buy stocks. It works out pretty well desu

>>9051402
yeah I guess it does sound pretty cool thanks bud

>>9051402
>>9051442
Holy shit.

>>9046534
>product of [math] x [\math] and [math] y^{2} [\math]

does electricity flow from one direction to another like in a river, or is it better to think of it as just appearing and disappearing in a circuit?

Ill never understand fucking electricity. How can positive charge even flow? Protons cant even move. It makes me feel really sad to not know and understand this shit.

Need help with an abstract algebra problem:
If [math]G[/math] and [math]G^{\prime}[/math] are groups with normal subgroups [math]H[/math] and [math]H^{\prime}[/math] respectively, and [math\phi[/math] is a homomorphism of [math]G[/math] into [math]G^{\prime}[/math], then [math]\phi[/math] induces a natural homomorphism [math]\phi_*:(G/H)\rightarrow(G^{\prime}/H^{\prime})[/math] if [math]\phi[H]\subseteq H^{\prime}[/math]

I'm not sure what this homomorphism is supposed to look like, let alone where to start on the problem itself.

>>9051934
is it not just the obvious
gH -> phi(g)H'

>>9051912
I'm not exactly an expert on this stuff, so take everything I say with a grain of salt, but I'll try my best to answer.

Electricity does flow. Protons stay where they are. Think of a racetrack where electrons are the cars and protons/neutrons are the track. As the cars move around, they create a positive charge in their wake; after all, if you move an electron away from something, you're left with an increase in positive charge.

All of that might be wrong, but that's how I understand it.

Ok if elements like 115 last for nano seconds or whatever?

When do they exist normally and where do they exist?

and if you can just keep adding protons to form new elements does that mean their is an infinite number of elements?

>>9051912
Yes. You can make an analogy of electron flow with water current flow, but it has some limitations since they're obviously different mediums. One of the main differences being that the electron flow seems instantaneous to us and the flow stabilizes itself quickly. It's better to just assume that it dissapears and appears if the circuit is closed.

The convenient current flow bullshit is just an extension of the problem about defining eletrons as "negative charges". It is a problem we have in physics which no one bothered to fix (at least, that's how I see it). Ultimately, the charge inversion doesn't do anything besides making electricity a bit more hard to learn anyway.

>>9052088
>When do they exist normally and where do they exist?
They don't.

>and if you can just keep adding protons to form new elements does that mean their is an infinite number of elements?
No, there are limits to how much mass a atom can have for it to remain stable.

>>9049537
Electricity flows through every path possible, even air, although the resistance is so high the current would be negligible. Not sure whether the fork in socket would harm someone. More current paths only lessen the equivalent resistance, so it only adds to current for the same level of voltage.

>>9052102
Meant to reply to:
>>9049666

>>9052099
>They don't.

So unless we make them they don't exist?

>>9052111
Possibly, but I think someone who studies astronomy might have something to add about this. On earth, it surely doesn't.

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Brainlet in need of help:

The books says the answer to the 2nd question is [math]0,4 \cdot 10^4 cm^3 [/math] as the uncertainty of the measurement. The closest I could get to the answer is [math]0,04 \cdot 10^4 cm^3 [/math].

Can someone confirm that the book answer is correct or if it's actually incorrect? If it is any guidance would be appreciated.

>>9051935
Can't that be shown to be a homomorphism without assuming that [math] \phi[H]\subseteq H^{\prime} [/math] though? I figured I'd have to use that in the proof

>>9052170
if phi(H) isn't in H' then there's some h in H with phi(h)H' != H'

but since h is in H we have hH = H -> H'

>>9042819
Let S be the set of all people,
let T(x,y) mean "x trusts y", then:
[eqn]\forall x\in S\exists y\in S: T(x,y)[/eqn]

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?

Suppose that I have a sequence of curves [math] f_n [/math] and a curve [math] f [/math] both defined in [math] [0,1] [/math].

If [math] f_n(0) [/math] approaches [math] f(0) [/math] and [math] f_n(1) [/math] approaches [math] f(1) [/math] and the arclenghts of the sequence of curves approach the arclength of [math] f [/math] does that mean that [math] f_n [/math] uniformly converges to [math] f [/math]?

>>9039057
in a more general setting, why is the line A between two points on a line B, a subset of line B.

Does anyone have resources on how to do vector problems? Also anyone have a pdf solutions for young Freeman 14th edition university physics?

How do I use the monotone semiflow theory to establish a threshold type result on the global dynamics of the following SIS epidemic model defined on [math]W = [0,1]^{n}[/math] :

[eqn]\frac{dy_{i}(t)}{dt} = (1-y_{i}(t))\sum_{j=1}^{n}\sigma_{i}\lambda_{ij}y_{j}(t) - \mu_{i}y_{i}(t), 1 \leq i \leq n [/eqn]

It is given that all constants are positive real numbers and the matrix [math]\Lambda := (\sigma_{j}\lambda_{ij})_{n\times n} [/math] is irreducible.

If you put hot water in a tray in the freezer it turns to ice faster than if you put cool water in the tray into the freezer?

What exactly does a Laplace Transform accomplish? I don't mean literally, I know it transforms a function in terms of t to a function in terms of s. I'm just having trouble understanding the point from a pure mathematical perspective. For example, a derivative gives you the slope, an integral gives you the area, what does a Laplace transform give you?

>>9052713
From wikipedia:
>The Laplace transform is very similar to the Fourier transform. While the Fourier transform of a function is a complex function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable. Laplace transforms are usually restricted to functions of t with t > 0. A consequence of this restriction is that the Laplace transform of a function is a holomorphic function of the variable s. Unlike the Fourier transform, the Laplace transform of a distribution is generally a well-behaved function. Also techniques of complex variables can be used directly to study Laplace transforms. As a holomorphic function, the Laplace transform has a power series representation. This power series expresses a function as a linear superposition of moments of the function. This perspective has applications in probability theory.
The Laplace transform is invertible on a large class of functions. The inverse Laplace transform takes a function of a complex variable s (often frequency) and yields a function of a real variable t (time). Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.[1] So, for example, Laplace transformation from the time domain to the frequency domain transforms differential equations into algebraic equations and convolution into multiplication. It has many applications in the sciences and technology.

Anyone on /sci/ major in geography or atmospheric science?
pls no bully

>>9052730
So if I'm reading this correctly, the Laplace Transform is another way to look at functions analytically?

>>9049898
Universe is very large compared to earth-moon distance so its not noticable by people, even moreso distance between subatomic particles. There's a reason we have to use cosmic microwave background to figure out the universe is expanding.

I want to go to uni for physics, however i am currently in my last year of school and not in the perquisite classes, or even have enough advanced classes for direct entry(ATAR, Australia)

I'm going to look for ways to get in next year regardless, but i need to know senior high school physics and somewhat advanced maths(Mathematics methods is the course name), if i cant ill just spend a year or two getting a shitty engineering diploma and apply again.

Tldr; Can you provide me with some links or info for upper school physics and maths(Maybe a little chemistry too) to transition into a physics course at university

>>9052752

A typical Calc I/II + Intro ODE should be sufficient for entry level physics.

>>9052088
>>9052099
They do, in violent hypernovae or big accretion disks.

When a star fuses its not because of pure chemical reaction - it's because electrons can tunnel into the nucleus of an atom, and if they already have a lot of energy and mass, it happens semi-frequently (hence why stars burn slowly; there arent that many reactions compared to the number of atoms in the star)

Same thing happens near extremely violent phenomena - they're formed but only in very very small quantities and quickly split apart.

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So there are ion channels that are permeable for Calcium, some are permeable for Potassium, some for Sodium. But how are they selective to begin with? A small ion would easily pass through the channel pore made for an cation with a bigger ion radius.

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>>9050567

help me lads

>>9052763
I can see those on khan academy, is that enough?

>>9052794
If you're referring to the channels which are sensitive to changes in membrane polarity, then yes. I think the only reason they are called that is because Sodium ions are the main positively-charged ions driven into the cell when those channels are open.

As for channels that use ATP to take those ions out and into the cell artificially, they only open once they get connect with the specific ion. So yes, those are selective.

>>9052688
No...? Cold water freezes faster. It's a lower-energy system.

>>9052928
So when e.g. a voltage gated calcium channel opens, it lets sodium pass, too?

>>9053209
https://en.wikipedia.org/wiki/Voltage-dependent_calcium_channel
>These channels are slightly permeable to sodium ions, so they are also called Ca2+-Na+ channels
Apparently, yes.

>>9053287
>>9052928
thank you

>>9039057
Such a scary pic!

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Are nuclear explosions visible through the walls of buildings?
I don't mean, can gamma rays penetrate walls or how far away a wall has to be before it won't be destroyed, I mean if you're near a nuke blast and you're facing the explosion but a wall is between you, will it still be visible?

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how does this work?

center of mass directly below the fingertip?

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>>9050567
>>9052801

This is the cutest girl in my folder of girls I use for attracting attention on worksafe boards...

If I didn't word the question correctly I can take a picture of the book

>>9050677
I don't see much wrong with that proof. You need to already accept that if lim f(x) =a, and lim g(x) = b, then both lim f(x)+g(x) = a+b and lim f(x)g(x) = ab. (All limits when x goes to the same value.) The author appears to be trying to keep to this limited set of facts about limits, and also avoiding going down to the epsilon-delta level.

Can I clean an aluminium mousepad with 96º ethanol?

>>9054626
yes it's metal. metals are inert.
it's plastics with color prints that could become problematic. or fabric/paint, especially with acetone (nail polish remover).

>>9054661
>>9054626
* but dont use acids on metal however

>>9039626
Yes. You only need one counterexample for the inclusion to not be true in general. Though, you can come up with examples where it does hold.

>Podcasts

I'm looking for podcasts that can teach me crap
Are these physics podcasts good or filled with misinformation.
1. Ask a Spaceman!
2. The titanium physicists
3.Star Talk

>>9054735
Any popular science source is going to have misinformation, not because they're necessarily wrong, but because they dumbed-down interpretation they give isn't really the full picture. Hence why there are so many fedoralords running around spouting bullshit about quantum physics and astronomy. Truth is that any science is complex and takes a long time to understand. You can't learn these things in an hour.

That said, they may be a good exposure to the concepts. Remember that anything they teach will only be half of the story, and you can't claim that you really know anything about it. If you ever want to dig into something and really learn it, your best bet is with textbooks, lectures, courses, etc.

Anyway, I can't give you advice on those podcasts. I listened to like the first 10 minutes of a Star Talk episode but I couldn't stand the Grasse Tyson's voice. These aren't podcasts, but the Youtube channels PeriodicVideos, Numberphile, SixtySymbols, etc. (there are a bunch of other channels by the same guy) are unironically pretty good. Don't get fooled by the Numberphile memes on /sci/.

Actually, for podcasts, Stuff You Should Know is pretty chill. But the guys just do "research" (aka reading articles online) on the topics for about a week, so it's really just pseuds teaching other pseuds.

>>9055044
Thanks a lot
I have a up to date high-school textbook, for more should i just go to /lit/ or is there some link floating around here

>>9055065
/lit/ won't be of much help.

Use libgen.io to steal books.

http://4chan-science.wikia.com/wiki//sci/_Wiki has textbook recommendations.

Why is CH2OH is polar but not charged, while is CH2COOH charged in an aqueous solution? I imagine the CH2COOH loses the H proton, but why does CH2OH not lose it too? Is it because -OOH is a lot more electronegative and H cannot hold to its electron?

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https://www.youtube.com/watch?v=aOENUWCxfqA

i-is this true?

a-asking for a friend.

>>9040546
browse google scholar for relevant publications and start sifting thru highly cited works and authors

>>9055765
degenerate

>>9055592
>Is it because -OOH is a lot more electronegative and H cannot hold to its electron?
i would think also because it has resonance, delocalizing the charge is possible while with CH2O- it's not.

>>9051323
Accepting more responses for this please

Okay, here's a stupid thought I had while watching Space Balls last night:

Suppose I have a cubical container traveling at the speed of light. It is filled with pure oxygen, and the walls have no imperfections.

Theoretically, how would the light inside the box respond? Would the box become dark? would the light be pushed to the end of the box? What if the box was perfectly translucent? Would it leave a trail of light behind it?

What about sound waves? Would the travel differently inside the container?

I'm no physicist, but I figured it was worth asking.

2 blue marbles and 6 red marbles, 8 total

What is the chance you get the 2 blue marbles choosing 3 at random from the 8 total?

I tried to do it two different ways but am getting different answers.

With permutations:
8p3=336
Number of permutations including 2 blue marbles:
b1,b2,r1...r6
b2,b1,r1...r6
b1,r1...r6,b2
b2,r1...r6,b1
r1...r6,b1,b2
r1...r6,b2,b1
=36
36/336=.107

With fractions:
Looking for ways to fail to grab 2 blue marbles:
0 blue marbles:
((6/8)(5/7)(4/6))
1 blue marble:
((2/8)(5/7)(4/6)) or
((6/8)(2/7)(4/6)) or
((6/8)(5/7)(2/6))
Sum all those together to get .798
1-.798=.202

So is it .107 or .202? My instinct tells me it's .107 because of the simplicity of the calculation, but I'm not sure and feel like combinations are a better way to solve this than permutations.

>>9056180
>Suppose I have a cubical container traveling at the speed of light.
Already impossible. Only light can travel at the speed of light. You cannot make a box out of light.

>>9056246
>Suppose
I never said it was possible. I just wanted to know what would happen if it were possible.

>>9048248
No you lazy mongo, the whole point of that exercise is to show you that using Riemann sums gives you the same answer

>>9049770
Griffiths book on QM is pretty easy to read for undergrad level shit

>>9048248
Sure, as long as you understand that the concept of integrals is separate from the concept of antiderivatives, and they only happen to be connected because of the fundamental theorem of calculus.

Approximation techniques for integrals are used quite frequently. Many functions are hard to antidifferentiate. Computers help a lot with said approximation techniques, though.

Why doesn't space tear stuff apart as it expands?

Hello,
how would I go about converting the main formula that talks about force and velocity, to torque and angular velocity?

https://physics.stackexchange.com/a/196123

>>9056260
If your head turned into an airplane, would the landing gear be down?

I'm not saying that it's possible, just asking what would happen if it was.

Why do fish have 4 pectoral fins?

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I accept that [math]E[E[X|Y]] is E[X][/math]
and expected values of linear combinations e.g [math]E[aX+bY+c] is aE[x] + bE[Y] +c[/math]

but I do not understand conditionals. Can you distribute/use/copy (I am sure there is a fancy word for it if you can) them inwards? Doing that is the only way I have made sense of the step from the original black 4th to last line.

of course I have derived the steps in between in a pretty roundabout way only applying one of the two rules above at a time, but have I understood it correctly as is?

>>9057615
also I suppose this means the expected value in markov processes is the same expected value from statistics ?

>>9039057
Isn't this obvious since it's intersection, intuitively on the left you are intersecting a smaller family, and on the right you are intersecting the bigger family, which should be smaller.

>>9056260
When you ascribe mass to something that moves at the speed of light, all physics breaks down and even your hypothetical question becomes unanswerable. It's maybe something like asking what would happen if atoms didn't exist. It's that fundamental.

>>9056479
The expansion only takes place over huge distances. The reason we can see it (faintly) between galaxies is because the distances between them are absurdly large. The main thing to remember is the calculus behind this: The rate of expansion of the Universe doesn't just increase with time; it increases with *distance* as well. And you need a hell of a lot of distance to notice anything at all.

>>9057482
It would depend on the state of flight.

Currently, I am on the ground, meaning the landing gear would likely be engaged.

>>9057745
I never said the object had to have mass.

I tried my best to simplify the question as much as possible, I.E. only measure light and sound, leave the rest out of the question.

The source of the light can't exist either.
It has no mass, casts no shadow, and evenly spreads an infinite amount of light inside the container.

Just because something doesn't happen does not mean we cannot speculate what would happen if it did.

>>9044073
I don't believe many engines actually limit the amount of time in a game.

However, I would not be surprised if it did take into account the time to this point and / or the time remaining.

Most decent chess engines almost certainly look at your mistakes, though not very deeply. I'm thinking it's either two or three moves deep.

>>9042915
Assess your intelligence honestly and don't be afraid to make an honest living out of something appropriate for your capacity, even if it's not a intellectually challenging job. Then in your free time study mathematics as advanced as you can.

Is it possible to go with an undergrad on EE (or masters? 5 1/2 years) to apply for a PhD in physics?

>>9058795
>(or masters? 5 1/2 years)
Not sure about a bachelor's, but that seems almost overqualified. It depends on your grades though, really.

>>9058877
Eh, third world education is different (not better) than Murica's.
For example a Bachelor of science, lets say, compsci = 5 years, an Engineering degree 5-6 years (or more because life).
What concerns me is that I've only two courses of physics, I guess it covers classical mechanics, and then everything related to EE, I guess, but nothing more advanced. I don't have problems with studying on my own during the summer or doing whatever is needed, unfortunately we don't have GRE or similar to prove our prowess in 'X' subject, and that's what I'm worried about.
I could go with NukE but considering that in the grand scheme of things, NukE is quite limited on its reach, I would rather stay with EE which have more Interdisciplinarity (is this even a word?).

>>9058891
Well I just compared our program with MIT's, we see the same physics as the guys from EECS do, I guess that will give you a better idea of my position.

>>9053504
yes.
also, if centre of mass is lower than axis of rotation, in ths case the finger, gravitational force is restorative. So you can prod it and it will come back to this position

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Why did /mg/ get deleted?

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>>9039057
>>>9059066

>>9059091
The janitor/mod was too lazy to delete only the off-topic posts made by the cancerous 2huposter and the kancollefag.

>>9053794
I want to lick her bracers while I fondle her boobs.

>>9049898
Inflationist models are bullshit.

Does anyone have a good reference for differential equations of the form [math] Y_t = f(Y_t) dX_t [/math], where [math] X [/math] is some deterministic process (i.e. not stochastic)? They don't seem to have a 'name' (as opposed to, say, ODEs or SDEs), so searching for stuff on them is difficult.

>>9059219
Functional equation.

>>9044080
Look at the population leading up to the Holocaust and see whether it's consistent with exponential growth. If so, you're safe just extrapolating from that.

>>9046968
They're usually assumed to use one-time pads, which are completely unbreakable even in theory -- you can't know whether "*******" is "ATTACK!" or "RETREAT" without the key.

>>9059224
That doesn't seem to be what I'm looking for; I was hoping more for something that lists possible approaches to define the integral depending on the properties of [math] X [/math]. Thanks either way.

What is a long calculation that I can use to benchmark a processor, not containing any random numbers or trigonometric functions?

>>9050594
Short answer: yes.

Long answer: ground and voltage are relative concepts. Voltage doesn't really exist "at" a place in the circuit, only voltage changes across components do. For the purposes of an abstract network analysis problem like this one, the only function of a ground is to give you an arbitrary zero point to compare other voltages to, which in this circuit would indeed conventionally be at the negative terminal of the battery. However, since the ground isn't there, it could TECHNICALLY be a zillion volts at the negative terminal, a zillion plus ten at the positive terminal, etc., or negative a zillion at the negative terminal, etc.; but this is stupid and would only be the case for a really dumb trick question, since the negative terminal being zero volts in this case is so obvious that eliding the ground symbol is pretty common. In an actual physical scenario, if the circuit isn't grounded it could theoretically build up voltage and shock you when you went to measure it, but this is unlikely to happen to any noticeable extent unless the circuit floated through a vacuum from some parallel dimension of excess charge.

(There's an analogy between the arbitrariness of "absolute" voltage and the constant of integration of calculus, if you're feeling mathy.)

>>9052583
I don't know jack shit about sequences of functions, but my VERY strong geometric intuition is no: you can easily draw a quarter-circle arc from (0,0) to (1,1) in two different ways, and these will have the same arc length and the same endpoints. So take [math]lim_{n \to \infty}f_n[/math] as one arc and [math]f[/math] as the other, and you have a disproof by counterexample.

>>9053066
https://en.wikipedia.org/wiki/Mpemba_effect

>>9055765
you would have to swallow a LOT of jizz for it to be nutritionally significant, probably more than anyone ever has, but you're on 4chan, so good start I guess

>>9042918
Bob

>>9052583
not at all and you should be able to figure out why

If I dug a hole 5cm deep of soil, is there a way for me to figure out how long ago that 5cm deep patch was on the surface?

>>9056878
>Note that I modified the equation given in the reference slightly - it was showing the torque for a rotating disk, from which I deduced the force
You may want to check that reference, or deduce it multiplying by the distance.It's likely the moment of inertia is going to show up.

>>9050594
If you measure the voltage between /any/ two points in two isolated circuits, you're going to get a zero reading. The concept of potential difference doesn't exist without a common reference.

Also: the concept of potential only exists in a potential field, one where the electric field is the gradient of a scalar function. This excludes any circuit which intersects lines of magnetic flux.

If you flipped a coin an infinite number of times, and arranged the results in a sequence, could you assume that this sequence contains somewhere within it an infinitely long sequence of only heads being flipped? (Assuming 50/50 odds of heads or tails on each flip.)

>>9057615
Never took a formal course on Markov processes, and I've never seen the notation before, but I took stats so I'm going to attempt a guess anyway:
That step is probably a case of [math]v(S_{t+1}) = E[G_{t+1} | S_{t+1}][/math]
(the time subscript can be anything because Markov)
and since [math]S_{t+1}[/math] and [math]G_t[/math] appear to be nonrandom function of [math]S_t[/math], it seems that conditioning on [math]S_t=s[/math] makes [math]E[G_{t+1}| S_{t+1}] = G_{t+1}[/math] into a constant.

In any case, since the derivation takes up a single step on the slide, you should not be expecting any complicated substitutions or expansions.

>>9057621
yes

>>9059580
No. That would imply that only a finite number of tails came up. Any infinite subsequence of flips has to have both tails and heads.

>>9059600
> infinite subsequence
of consecutive members.
You can have a subsequence of only heads, but they'd be dispersed among tails entries.

>>9059580
If you're asking if [math]every[/math] infinite sequence of coin flips (even if it's a fair coin) contains an infinite sequence of heads, then the answer is trivially no: consider the sequence HTHTHTHT...

If you're asking whether such a sequence [math]exists[/math], then you can trivially construct such a sequence, but my intuition is that "almost all" sequences are not of this form, i.e. that the probability of getting such a pathological result, for a [math]particular[/math] infinite sequence of flips, will be exactly zero.

>>9059606
Your example contains an infinite subsequence of heads (given by the odd positions in the sequence).
> you can trivially construct such a sequence
No. Suppose there [math] \exists n \in \mathbb{N} [/math] such that [math]\forall s \in (s_{n+i})_{i \in \mathbb{N}},\ s = \text{heads} [/math]. So tail results are finite, which is false.

In fact, almost all infinite subsequences of coin flips contain heads, and almost all infinite subsequences of coin flips contain tails. There is exactly one subsequence in each case for the case where this does not happen (the subsequences of heads/tails results respectively.)

>>9059629
You can of course construct a sequence that has an infinite number of consecutive heads results and then an infinite number of consecutive tails results, but you'd have to use transfinite induction. The model would be immaterial since no completed infinities of coin flips can exist.

What's *the* most fundamental mechanism that gives some material its properties?

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I need some help figuring out if I'm fucking up with Financial Aid for school
I'm going to a public state school in PA for a Bachelor of Science and am staying on campus with a meal plan etc. In total my bill per semester is about $16k but my financial aid only covers about $10k meaning I would have to take out a loan for $6k each semester.
I am going to be a Sophomore in the Fall and I remember my mom saying she took out around $14k for me in the Parent PLUS loan last year, meaning if I have take out another $12k to pay this year I would already be at $25k+ on debt not including the non PLUS loans.

And from googling around $20k-$40k in debt is what people typically finish school with, not have by Sophomore year. I'm wondering if I'm just retarded and this is normal or there is something wrong. I made a similar post here before and someone blamed it on "The College Experience" being more expensive than normal, but I don't think that's it.

Pls no bully

>>9059595
He did mention law of iterated expectations was used in the last step ( https://en.wikipedia.org/wiki/Law_of_total_expectation ), though I am not sure how the conditional fits into that if it appeared in the outer expression, or if you can apply it to expressions appearing inside that expression as well, if that makes sense (like I have added in purple and red)

>>9050677
its ok the epsilon delta proof is really gay and no one really understands it

Someone please help. What the hell does this mean?? English is not my first language btw

>s = 0^p 1^p 0^p 1^p, s = uvxyz

>First, we show that the substring vxy must straddle the midpoint of s. Otherwise,
if the substring occurs only in the first half of s, pumping s up to uv2xy2z
moves a 1 into the first position of the second half, and so it cannot be of the
form ww. Similarly, if vxy occurs in the second half of s, pumping s up to
uv2xy2z moves a 0 into the last position of the first half, and so it cannot be of
the form ww

what does he mean by straddle the midpoint? 0101011 and 0010101?

>>9059775
I recommend buying a gun and storming into the university where you'd shoot the entire administrative staff. It's beyond me how you murricans cuck yourselves with these prices for education.

Any biology fags here?
>inb4 not a real science
first time posting. I currently work on my bachelor thesis and do a lot of phylogeny based on DNA sequences of fungi.

my question is: is there a significant difference between the influence of single nucleotide polymorphisms and gaps in the alignment on the placement of species inside the tree?

I would have expected that sequences with more gaps place further away from one another than sequences with more SNPs.

what I experience is that sequences of the same species which are similar, but have different gaps, place more closely together than sequences of the same species which are similar but have more SNPs.

honestly this confuses me, would've thought that gaps are generally more influencial than SNPs

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These are some books I kept from my time in community college. I’ve got linear algebra, differential equations, and a big-ass tome of lowish-level calculus. I dropped out of for-real University about a year into it, and it’s been about 4 years since then. My goal now is to git gud enough at math to both regain the knowledge I’ve lost (so basically all of it), and hopefully get a little head-start on the classes I haven’t taken yet. Is it doable?

Also, each of the books has over a dozen chapters, but the professors would only give homework for 4-5 at the very most. Will it help to go through the entire books, or do you think those chapters were omitted for a reason?

>>9039057
More intersections means getting smaller

>>9056278
Oh my fucking god i love you, thanks anon

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What happens if I just take melatonin everytime I wake up so I can just sleep forever, stopping only to eat, pee, and bathe?

>>9059990

what is it supposed to be about

are you describing an algorithm? which algorithm?

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Do junkies use drugs, or do drugs use junkies?

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>>9039057
what the fuck? I feel like they just started pulling numbers out of thin air for this one.

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>>9061195
>I feel like they just started pulling numbers out of thin air for this one.

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>>9061198

>>9061195

[math]a(b+c) = ab+ac \\ \\ (x-2)(x-2) = x(x-2)+-2(x-2)[/math]

>>9061206
I see it, kinda, but why?
The primary example without variables is solvable, the example with variables is not inside the parenthesis.

Why are these things?

>>9061217

The first line is not solvable, it is not a question. It is a true statement.

as for "why":

Imagine you are talking to a kid and they ask you questions.

They say "Why is the sky blue?"
"Because it is made of blue shit"
"Why is it made of blue shit?"
"Because the earth was hit with a blue asteroid"
"Why was...."

Eventually you will get down to some fundamental assumption.

All I'm going to say is that math has a fundamental assumption as well. Things are constructed from that.

Properties such as this one have proofs, but they involve mathematical concepts you don't know about that are closely related to the formal definition of this basic assumption that math is based off of.

https://en.wikipedia.org/wiki/Peano_axioms#Arithmetic

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>>9061314
The sky is blue because the wavelength for blue is weaker than other colours and defuses in our atmosphere sooner.

There's a reason things are the way they are, or at least an observable cause. I'm not being pedantic I'm genuinely confused as to why you do it that way so I can replicate it with other problems.

in short, I can understand up until the point that -2x -2x isn't -4x squared. Which is still two steps farther than I was before.

>>9061365
>why you do it that way
Because you're working in a ring.
https://en.wikipedia.org/wiki/Distributive_property

Can someone explain theorem 2.41 of baby rudin?
https://math.stackexchange.com/questions/341521/baby-rudin-theorem-2-41
>Then S is infinite (otherwise ... for infinitely many n)
I know S is infinite since every neighborhood of [math]x_0[/math]must contains some points of E.
But I don't understand Rudin's argument.

>>9061521
The condition [math] | x_n - x_0 | < \frac{1}{n} [/math] can only be fulfilled if you use infinitely many [math] x [/math]. Otherwise there is a lower bound, and this contradicts our choice of the sequence.

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>>9061521
Think about compact sets as spaces with hard walls.
Think about non-compact sets as a country's airspace. Airspaces have no hard boundaries.
>I don't understand Rudin's argument.
He wants to prove [math] (a) \implies (c) [/math], which is equivalent to proving [math] \neg (a) \vee (c) [/math]. So he proves that [math] \neg (c) \wedge (a) [/math] leads to a contradiction.

>>9061544
My apologies, he wants to prove that [math] (c) \implies (a) [/math] so he proves that [math] \neg (a) \wedge (c) [/math] gives a contradiction.

>>9061537
>>9061544
I want to know whyotherwise [math]|x_n−x_0|[/math] would have a constant positive value, for infinitely manyn
and what's wrong with it

>>9061555
Imagine you have [math] p [/math] points in [math] \mathbb{R}^k [/math] and an infinite sequence which just cycles through these points. So forget about the sequence and just think about [math] \| x_0 - x \| [/math] where [math] x [/math] is one of those points. You only have [math] p [/math] such distances between [math] x_0 [/math] and the points, so it cannot be true that you have points in the sequence which are at distance at most [math] \frac{1}{n} [/math] from [math] x_0 [/math] for any [math] n [/math], because that hypothetical distance can get however small, but you only have [math] p [/math] fixed distances for [math] p [/math] points.

>>9061555
The sequence [math] (x_n)_{n\in\mathbb{N}} [/math] is chosen so that [math] |x_n-x_0| [/math] goes to zero. If [math] S [/math] is finite, then there exists [math] m [/math] such that [math] x_m = x_{m+1} = x_{m+2} = ... [/math] (because you 'run out of points'), and hence [math] |x_n-x_0| [/math] is constant for [math] n \geq m [/math]. Since we have chosen a sequence that fulfills [math] |x_n-x_0| < /frac{1}{n} [/math], this (i.e. [math] S [/math] being finite) cannot be the case.

>>9061564
Thank you.
Can I just say that S is infinite since every neighborhood of[math]x_0[/math] must contains some points of E.

In all honesty Rudin's argument is fucking retarded. Any sequence of finite points can only have as a limit point one of those points, since as anon observes here >>9061564 after a certain rank the sequence will always just take one of the points as a value. Otherwise it is divergent.

So the proper argument he should have made was that were [math] S [/math] finite, it couldn't have a limit point that is not itself contained in [math] E [/math], after which he would have went on to prove that the case for an infinite [math] S [/math] also gives a contradiction.

>>9061571
That's exactly the argument Rudin makes. So yes, you can.

>>9061571
>>9061576
To clarify, the condition [math] |x_n-x_0| < \frac{1}{n} [/math] just says that for every [math] n [/math], the neighbourhood [math] B_{\frac{1}{n}} (x_0) [/math] contains an element of the sequence.

>>9061580
Then there is no need to prove that S is infinite since it is so by definition.
Rudin sucks. How in the world did this garbage even become a meme?
Find a better textbook.

>>9061588
>Then there is no need to prove that S is infinite
There is, though. S is only infinite because the limit point is not contained in it. For a general sequence [math] y_n [/math] with [math] |y_n - y_0| < \frac{1}{n} [/math], it is still possible that [math] y_n = y_0 [/math] for all n greater than some m. Then S would be finite.

>>9039057
Given P(A|B) > P(~A|B) and P(~A|~B) > P(A|~B) can you prove P(B|A) > P(~B|A)?

>>9061644
No, because it's not true.

Counterexample:

P(~A&~B) = 1/2
P( A&~B) = 1/4
P(~A& B) = 1/12
P( A& B) = 1/6

P( A) = 1/4+1/6 = 5/12
P(~A) = 1/2 + 1/12 = 7/12
P( B) = 1/6 + 1/12 = 1/4
P(~B) = 1/2 + 1/4 = 3/4

P( A| B) = P( A& B)/P(B) = (1/6)/(1/4) = 2/3
P(~A| B) = P(~A& B)/P(B) = (1/12)/(1/4) = 1/3
=> P( A| B) > P(~A| B)

P( A|~B) = P( A&~B)/P(~B) = (1/4)/(3/4) = 1/3
P(~A|~B) = P(~A&~B)/P(~B) = (1/2)/(3/4) = 2/3
=> P(~A|~B) > P( A|~B)

P( B| A) = P( A& B)/P(A) = (1/6) / (5/12) = 2/5
P(~B| A) = P( A&~B)/P(A) = (1/4) / (5/12) = 3/5
=> P( B| A) < P(~B| A)

>>9059254
That reminds me. Grounding the circuit wouldn't just make the circuit's current dissipate into the ground? I don't remember how this would make the circuits safer or how it wouldn't ruin the circuit.

>>9059576
>If you measure the voltage between /any/ two points in two isolated circuits, you're going to get a zero reading
So, does that mean that putting a voltmeter on the literal earth and on any part of the circuit would deliver a zero reading anyway?

I still don't understand how voltage should be arbitrary, especially how the second law of Kirchoff is supposed to work in this. Do you guys know a good place to explain this?

I am not sure exactly how to explain this, but I am wondering if it would be possible to use a Radioisotope thermoelectric generator utilizing a short half life fuel like 254Fermium to deliver as much power as a 80kN turbofan engine over a period of three hours, and how much fuel mass that would require.

For the purposes of this thought exercise I am assuming that the RTG has an efficiency of 40%.

Thanks.

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Why is Matlab not plotting the graph correctly?

I have a scatter plot with four points and am using polyfit and polyval to get the 1st order line of best fit, but it's ridiculously offset.

>>9062138
Found the issue:
it was
plot(temp_vector, polyval(Fit, temp_vector))

I was just plotting Fit by itself. I'm a dumbass

>>9061807
> So, does that mean that putting a voltmeter on the literal earth and on any part of the circuit would deliver a zero reading anyway?
Yes, because no part of that circuit is grounded.

In order for a voltmeter to show a non-zero reading, there must be a non-zero current between the terminals. For an electronic voltmeter, that current could be minuscule (a picoampere, or even less), but it must exist, and that would require a return path (i.e. a loop).

> I still don't understand how voltage should be arbitrary, especially how the second law of Kirchoff is supposed to work in this.
KVL requires a loop. If you connect two isolated subgraphs with a single edge, that edge cannot be part of any loop.

Can anyone post the math textbook list which starts at brainlet tier and ends with bourbaki?

>>9062200
I'll give you a (You) because I'm interested as well.

How do I ask a famous person for a letter of recommendation

I've known this person over email for a couple of months and done a lot of shit for/with/in correspondence with this person

Trig identities how do I prove that (secx+cscx)/(tanx+cotx) is equal to sinx+cosx