/sqt/ - Stupid Questions Thread: Contracting Homotopies Edition

I'm trying to quantify how much amperage a capacitor could push out, compared to a regular DC voltage source.

Say you charge a 100uf capacitor to 200 volts. We can get the energy in joules by: 0.5 * F * V^2 = 2J. Since 1J = 1W, does that mean that the maximum current the capacitor can dish out is W/V = 10mA?

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Could some of you /lab/ fellows answer the following questions:
>what are you majoring in?
>how many hours do study a week?
>best part of being in a lab?
>worst part?
>any regrets?

>>8637460
What exactly are you asking? If the complex is acyclic then t_n, so defined, is a contracting homotopy. The motivation is that it proves the theorem.

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>>8637587
>What exactly are you asking?
Obviously the definition proves the theorem, I'm asking how would one come up with such a definition of the [math] t_n [/math]?

>>8637506
a capacitor can dish out as much current as ohms law allows, but it will only be instantaneous as a capacitors voltage will drop with time

Vc is a function of time, and W has a dimension of time, so the equation W/Vc = 10mA doesn't really make any sense to me, there might be some use for it but I have no idea what the 10mA even signifies

>>8637614
I guess I was looking for a way to figure out how big of a capacitor I would need for it to be able to dish out as much current if you connected it to something for 1 second, as a regular power source.

Assume a reliable 10v power source connected to a 100ohm resistor for 1 second. That would be 100mA of power flowing.

Replace the power source with a capacitor charged to 10v. How many farads of charge would it need to be in that capacitor to be able to dish out the same current?

>>8637460
is earth rhombus?
will gw fags ever admit defeat?
when will atheists be able to define atheism?
is string theory really the most noble field of study?

>>8637643
>is earth rhombus?
probably not
>will gw fags ever admit defeat?
maybe
>when will atheists be able to define atheism?
eventually
>is string theory really the most noble field of study?
no

How the fuck do magnets work?

how do we solve the poo-in-loo problem? do we install subcutaneous mind control microchips that push the need for "self respect"?

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does jet fuel soften steel beams to the point of structural weakness to below it's design and ultimate F.O.S.?

>>8637460
It's fascinating that in the Stupid Questions Thread average IQ is about 20 points higher than the rest of the /sci/

how do i get A^2014?

A=[5 1 9, 0 5 1, 0 0 5]
>A -> matrix
what term should i search for to find solution for problems like this

>>8637698
https://en.wikipedia.org/wiki/Diagonalizable_matrix#An_application

The following are equivalent, right?
[eqn] \forall \epsilon > 0 ~ : ~ \exists \delta > 0 ~ : ~ \forall h \in \mathbb {R} : 0 < |h| < \delta \implies \frac { | f(x+h) - f(x) - Th |} { |h| } < \epsilon [/eqn]
And
[eqn] \lim _{ h \to 0 } \frac { | f(x+h) - f(x) - Th |} { |h| } = 0 [/eqn]

The first is clearly just the definition of a limit, with [math] c = 0 [/math]. But I don't see where the =0 part comes from.

>>8637687
Dunning–Kruger effect

>>8637677
Yes

>>8637623
>>8637629
any capacitor with an initial voltage of 10V will only produce 100mA of current for an infinitesimally small amount of time

the capacitor with an initial voltage of 200V would need to be 3.34 milliF to keep at least 100mA of current for an entire second or 500microF to keep an average current of 100mA

both of these would probably just burn the shit out of the resistor anyways

equation I used for this was
[math]I=\frac{V_0}{R}e^{\frac{-t}{RC}}[/math]
[math]C=-\frac{t}{Rln\frac{IR}{V_0}}[/math]

When do I start using series/sequences from calculus in future math classes?

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how the shit do I proof by induction pic related

>>8637782
Base case [math] n=2 [/math], [math] 1 + 4 < 8 [/math]. Well that checks out. Now we want to prove that [math] 1+ 2^2 + \cdots + (n+1)^2 < n+1)^3 [/math]. So we ASSUME that to be true and go from there. All you're really doing is a series of algebraic manipulations, so in your case: [eqn] 1+2^2+3^2 + \cdots + (n+1)^2 \\ = 1+2^2+3^2 + \cdots + n^2 +2n + 1 < n^3 + 2n + 1 ~\text { by the inductive hypothesis } \\ < n^3 +3n^2 + 3n + 1 \\ = (n+1)^3 [/eqn] The second line might trip you up, all that we've done is expand [math] (n+1)^2 [/math] and noticed that it gave us our original series, but with [math] 2n+1 [/math] added on the end. Since we assumed that [math] 1+2^2 + \cdots + n ^2 < n^3 [/math] it follows then that [math] 1+2^2 + \cdots + n ^2 +2n+1 < n^3 + 2n+1 [/math]. The chain of inequalities follows from the fact that [math] n>1 [/math]

>>8637831
>So we ASSUME that to be true and go from there

Sorry, that should be:
>We ASSUME [math] \sum k^2 < n^3 [/math] to be true.

I have a series of points that are uniformly distributed in a certain slice of the unit disk (y>=x>=0).
How do I calculate the covariance of x and y?

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>>8637831
>>8637836
I was following the example in the pic related (the white notes are from the video, the rest ugly written are my notes, sorry about that), from a youtube channel I found, so I proceeded likewise

but when I reached p^2 as you can see, I did p^2 + (p+1)^2

how wrong is that?

I can't do the fancy writing here, sorry, math is alien to me, but I'm trying to solve every exercise I'm given

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I'm supposed to solve this by Picard iteration, but what exactly am I supposed to use as my starting point? Using 0 will just continue giving me 0 for all terms in the series .. Or is that supposed to be the case? Can the other solution only be obtained via separation?

>>8637885
You could do it like that, but (imo) it's more cumbersome. The way I was thinking about it is:
>You don't care about the nth term anymore, just the (n+1)th term.

What they did in that video was to show that the [math] 1/(c+1)^2 [/math] term was just the original series with an added term. That's exactly what I deduced as well, except only by looking at the (n+1)th term.

If you wanted to to it the way you're doing it, then what you'd do is:
>Notice that [math] 1 + 2^2 + \cdots + n^2 + (n+1)^2 [/math] is the our original series with [math] (n+1)^2 [/math] added on.
>So we use our induction hypothesis: [eqn] 1 + 2^2 + \cdots + n^2 < n^3 \\ \implies 1 + 2^2 + \cdots + n^2 + (n+1)^2 < n^3 + (n+1)^2 \\ = n^3 + n^2 + 2n + 1 \\ < n^3 + 3n^2 + 3n + 1 \\ = (n+1)^3 [/eqn]
>Notice that in the second to last line we ended up in the same place as before.

And you're done. Does that make sense?

>>8637935
>And you're done. Does that make sense?

it totally does, beautiful, thank you anon

>>8637939
Good to hear. Induction can be a touch tricky when you first learn it because some of the ideas seem to come from nowhere (for example how did I know to massage [math] n^3 +2n+1 ~~ \text { into } ~~ n^3 + 3n^2 + 3n + 1 [/math]? Well the answer is I cheated, I looked at what I wanted [math] (n+1)^3 = n^3 + 3n^2 + 3n + 1 [/math] and then added the required terms. If you end up studying [math] \epsilon - \delta [/math] proofs, a similar "trick" is used then.

Also the "fancy writing" is scalled latex, it's not too hard to learn and is helpful when trying to communicate your ideas, especially over the internet. You can write inline by using [ math ] <text goes here> [ /math ] only without the spaces and block using [ eqn ] <text> [ /eqn ] again without the spaces. There's a bit of an issue with how 4chan parses your commands though so it's advisable to throw in whitespace everywhere, for example a fraction would be written as \frac { } { } instead of \frac{}{}.

>>8637949
you saved me, when I hit an exercise I can't solve, I cannot progress until I get it right

I've been meaning to learn a LaTeX, kinda feel like an idiot when typing "x^2"

oh well, thanks again, you've made my sunday

Given that I know [math]Pr(A)[/math], [math]Pr(B)[/math] and [math]Pr(A|B)[/math], how do I work out [math]Pr(A|B^C)[/math]?

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In logic, or propositional calculus, what is the difference between a transformation rule and a rule of inference?

https://en.wikipedia.org/wiki/Rule_of_inference

This page seems to list Rules of Inference as a subset of Transformation Rules (in the image on the right), but then in the first sentence implies they're synonyms.


Pls, satisfy my autism

A[1,2,2] and B[2,3,0] lie on p
C[4,0,5] and D[5,1,2] lie on q
p and q are skew lines and (1,2,3) is the direction vector of their transversal r
R[?,8,?] lies on r.

how do I find the distance |C,R|

I can't get this going at all

answer's supposedly sqrt20386

>>8637726
Anyone?

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Having a small physics problem (reposted from yesterday's sqt)
Okay, I'm having trouble witha simple physics problem:

The problem asks "What's the acceleration between the two blocks (which are connected by a pulley system)?" When I found the net force, the system moves in the direction of the 100kg block.

But here's where my problem lies:shouldn't the acceleration of the two blocks with different masses be equal? Intuitively, it seems difficult to see how F_net = ma applies here when the net force in the system will give different accelerations...

What am I doing wrong?

>the net force is applied to the combined masses, not the individual masses

=======
Anonymous 01/29/17(Sun)08:19:29 No.
Okay... Then to find the acceleration, would I do:

Mass 1 Net Force = (Net Force / Mass1+Mass2) * mass1
and
Mass 2 Net Force = (Net Force / Mass1+Mass2) * Mass2?

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I'm kind of confused about something.

How come the graph of sqrt(4-x) moves 4 units to the right instead of to the left? I thought anything under the radical or within parenthesis with an X moves the opposite direction of its sign.

We've not went over anything like this specific problem and I really don't understand why it would move like that.

The parent function would be sqrt X, I believe. I could be wrong. Don't recall if making the X negative counts as a transformation or not.

>>8637726
Yes, it's the definition of f'(x) converging to T.

Unless you're into a math major, epsilon-delta proofs are rather annoying and don't see much use. Just learn limit arithmetic and go from here.

>>8638309
The easiest way to find out why is working out the points on the graph yourself

>>8638309
Because [math] y=0 ~ \text { when } ~ x=4 [/math] I don't know how else to explain it.

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I'm having trouble understanding part of a proof of the Lyapunov function theorem (for non-strict Lyapunov functions). Pic related is a statement of the full theorem. Here is the proof I have:

By continuity of V, we can find [math]\delta > 0[/math] such that [math]|x| < \delta[/math] implies [math]V(x) < \epsilon[/math]. Then if [math]|x(0)| < \delta[/math], we have
[eqn]
\frac{d}{dt}(V(x(t))) \leq 0 \implies V(x(t)) \leq V(x(0)) < \epsilon \quad \forall t \geq 0.
[/eqn]
So we may conclude [math]x(t)[/math] is contained in the set of [math]\{x \in U \mid V(x) < \epsilon\}[/math].

We need to show [math]|x(t)| < \epsilon[/math] for all [math]t \geq 0[/math], but I don't see how that follows from what we've shown.

>>8638309
>I thought anything under the radical or within parenthesis with an X moves the opposite direction of its sign.
General advice: Don't think in such absolute terms. These "rules" work for certain given reasons - dig in and find out those reasons.

>>8638316
>>8638320
So if the x is negative it kind of reverses things? It seems kind of obvious now that I look at it when actually finding pairs. I had just assumed the "opposite whatever it's under" applied no matter what.

Does that mean sqrt-x actually was the parent function or did I have it right when assuming it was just sqrt(x).

It's been a while since I went over this stuff in detail, and right now we're at the stage of zooming pas everything to get to the new stuff, so a lot of examples are very brief.

Is it possible to live without consuming anything that was once part of another living thing?

>>8638366
Since you can't eat rocks, no.

>>8638338
I find it's helpful to try to think of these things more generally and then try to apply this to particular functions.

Suppose I have a function f(x). There are four simple ways to transform the function:
1) af(x). This "stretches" the function vertically by a factor of c. This occurs simply because you're multiplying each output of f by a.
2) f(bx). This "squishes" the function horizontally by a factor of b (relative to zero). This is because you're multiplying the functions input by b, the function will take on values b times as fast.
3) f(x + c). This will shift the function to the left by c. One easy way to see this is to realize that f will take on the value f(0) at x = -c in the new function. Realize then that this will happen with every point. If you want f(x+c) to take on the value f(t), you need x = t - c.
4) f(x) + d. This simply shifts the function up by d. This simply occurs because you're adding d to each output.

Here's a demo I made. I strongly recommend playing around with this until it makes sense to you and feels intuitive: https://www.desmos.com/calculator/v9vuw6mhlk

What's the actual definition of direct sum? My textbook says that
[math]
U_1 \bigoplus U_2=\{u_1+u_2 : u_1\in U_1,u_2\in U_2\}.[/math]
But looking up wikipedia, it mentions that [math]
\mathbb{R} \bigoplus \mathbb{R}=\mathbb{R^2}[/math]
but [math]\mathbb{R}\bigoplus \mathbb{R}=\{r_1+r_2:r_1,r_2\in \mathbb{R}\}=\mathbb{R}[/math] according to my textbook's definition. So what's the actual definition?

>>8638465
you actually take the disjoint union, the elements of the sets "don't mix". if they have the same elements you just force them not to be
it's as if you were actually adding Rx{0} and Rx{1} with your book definition

>>8638465
u1 + u2 should be taken as just a symbol. + should not be interpreted as the addition on the underlying group.

i.e. just think u1+u2 = (u1,u2)

So I'm really interested in sound (digital, analog, and such since I'm an EE) but I'm also interested in acoustics and how sound propagates in reality, how timbres changes depending on the surface, so on so forth.

So my question is does anyone know where I find a good acoustics book? Math preferred but not necessary

is there a nice guide on the internet out there to learn about doing statistics based shit in Excel?

Given that the measure for how acidic something is is H+ concentration, why are proteins that have more NH3+ groups basic?

Also, the dissociation constant for acids says your product is H3O+ and a corresponding A- base, but in protein the COO- deprotonated group usually signifies and acid (glutamate and aspartate).

I had a shit teacher in high school and I don't have a problem understanding most of biochemistry but this shouldn't be 'not-right', right?

>>8638672
http://lmgtfy.com/?q=statistics+in+excel

I wish people asked and others answered questions that can't be solved by google

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Am I retarded?

This answer is apparently wrong. But... the rank of the matrix is 2.

>>8638787
I believe your answer is correct.

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Can somebody please tell me where I'm misunderstanding this question before I punch a wall.

> probability that a dog is affected by a certain rare disease is 0.002
> probability of a test returning positive, given that the dog has the disease, is 0.99
> probability of a test returning negative, given that the dog does not have the disease, is 0.95
> find the probability that the test returns positive given that the dog does not have the disease

So we're working under the assumption the dog doesn't have the disease. Either the test returns negative or positive, right? So Pr(positive test, given that dog doesn't have disease) + Pr(negative test, given that dog doesn't have disease) = 1. Therefore the answer is 1 - 0.95 = 0.05. Only this is far too easy for the number of marks and the info given in the question, plus we're supposed to use Bayesian probability formulas. But surely those two probabilities *have to* add up to 1?

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>>8638813
>Pr(positive test, given that dog doesn't have disease) + Pr(negative test, given that dog doesn't have disease) = 1
wrong

they just need to add up to Pr(dog doesn't have disease)

which is why you use
https://en.wikipedia.org/wiki/Bayes%27_theorem#Statement_of_theorem

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>>8638818
>>8638813
btw i got 0.00051983967 doing it quickly

>>8637460
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4706048/

Does this mean precog abilities really exist?

>>8638818
>>Pr(positive test, given that dog doesn't have disease) + Pr(negative test, given that dog doesn't have disease) = 1
>wrong
>they just need to add up to Pr(dog doesn't have disease)

So [math]Pr(positive test | healthy dog) + Pr(negative test | healthy dog) = Pr(healthy dog)[/math]? Because I have the last two probabilities and the first one is what the question's still asking for. Which is obviously not right.

>>8638878
sorry i meant Pr(positive test & healthy dog) + Pr ( negative test + healthy dog) = Pr (healthy dog)

you cant add up givens like this since you move to a new probability space

>>8638787
You are right, A is the correct answer.

>>8638332
what the hell is [math]\dot V[/math]?

>>8638813
its 0.05

Did you misread the question? A more logical question would be:
> find the probability that the dog does not have the disease given a positive test.

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>>8638917
Maybe I'm misreading, but I don't think so.

>>8638903
Newton's dot notation, it means dV/dx.

>>8638903
>>8638961
Dot notation is really always used for a derivative with respect to t. To avoid this notation, the hypothesis is saying that [math]\frac{d}{dt} (V(x(t)) \leq 0[/math], where [math]x[/math] is a solution to the differential equation [math]\frac{d}{dt} (x(t)) = f(x(t))[/math].

>>8638945
Seems you haven't misread, it's 0.05.

You shouldn't overthink this,

Sample group: dogs without disease:
Given the test results either negative or positive.
P(negative)+P(positive)=1

It's the teachers own fault if he accidentally puts in an easy question like this.

>>8638981
Just solved it as a simultaneous equation, you're right. Fucking hell, I just spent 3 hours wondering why I was such a retard. Turns out I'm a retard in a completely different way.

>>8638978
Ok, but then what does [math]{\dot V}(x)\le 0[/math] for all [math] x \in D[/math] mean? How is [math] \dot V[/math] defined off the curve?

>>8639031
[math]<{\nabla V}(x), f(x)>\le 0[/math] for all [math]x\in D[/math]?

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Is time travel (into the future) possible?

>>8639031
That's correct. Also, you want \langle and \rangle.

>>8639042 should be replying to >>8639033.

>>8639035
probably not

>>8639035
As you read this sentence you have been traveling into the future.

inb4>How to make it faster?
idk

>>8639035
Not necessarily instantaneously, but if you go fast enough (approach c), you could experience time "slower" than say people on earth.

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Source: 'I F*cking Love Science'.

t. Average newspaper idiot

>>8639115
What the absolute fuck

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>>8638285
>Mastering Physics

I'm triggered

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>>8639120
Have another

>>8639074
You're looking for probability of not A and not B. You multiply when you want to know the probability of one event and another, so its:
[math] 0.6 \cdot 0.6 = 0.36[/math].
That is, there's a 36% chance of neither.

>>8639135
jesus fucking christ that word soup

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Could someone help me figure out what I'm doing wrong?

The question asks for the total charge of the rod, I plug in the numbers and it seems to give me a wrong answer

Pls respond

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So I think I need to revise how absolute values work.

With |a+b| is it not |0.9+ (-0.4), but then converted to 0.9+0.4 = 1.3 on the number line? Their answer looks approximate 0.5.
What is it that makes |a| + |b| = 1.3, and how do I get to the answer of 0.5 for |a + b|?

>>8639339
if a= 0.9 and b=-0.4 then
|a+b|=|0.9+(-0.4)|=|0.5|=0.5
and |a|+|b|=|0.9|+|-0.4|=0.9+0.4=1.3

>>8639345
I understand now. So you only convert the answer to positive after what was put in the bracket's expression is finished. Thank you.

>>8638032
[math]P(A|B^c)=P(A\cap B^c)/P(B^c)=(P(A)-P(A\cap B))/(1-P(B))=(P(A)-P(B)P(A| B))/(1-P(B))[/math]

Determine if the given function is a linear transformation.
T(x1, x2) = (5x1 + x2, −4x1 + 6x2)

what's the trick

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In Physics 3 right now doing a homework problem and have absolutely no idea what I am doing wrong.
The question goes:

What is the momentum uncertainty of a single photon in the pulse?

Given that the pulse has a duration of 8.60 fs and produces light with a wavelength of 496 nm.

The only equation in the book related to this section is in pic related and has not worked from my understanding of the equation.

>>8639679
just kidding I figured out what I had to do

>>8639482
>look at definition of linear transformation
>proceed

Brainlet here

How does the definite integral make your life easier in physics? I get calculating pi with a definite integral, but how it would be useful in a function of r, v or a over time doesn't click for me.

>>8639813
Nevermind, took 10 minutes to get it.

>>8638978
>>Dot notation is really always used for a derivative with respect to t.
source = undergraduate

>>8639813
>>8639856
now THAT was a stupid question

>>8637460
What is continuous map in topology and how maps work in topology space

>>8639893
preimage of open sets are open

We can define a number i such that i^2=-1.
What would it mean if we tried to define a number j such that j=1/0? Would it even make sense to do so?

>>8639897
assuming 0 is the number 0 in the reals.

division by zero is not defined in a field (the real numbers). So, no, it wouldn't make sense to do so.

>>8639897
doesn't give you anything particularly interesting, but you can read
https://en.wikipedia.org/wiki/Wheel_theory

>>8639902
I see, thanks.

>>8639871
I just realized it as well. Chapt 19 of Spivak is where it all really comes together clearly.

For the genes that are on the X chromosome in humans and other mammals, what are the differences in inheritance for males vs. females?

>>8639926
Male have XY while female have XX. Which means for recessive genes on the X chromosome men are much more vulnerable. One example is most forms of colorblindness. About 10% of the men have it, vs a tiny amount of women. While a non-X-chromosomal colorblindness variant is equally rare on men and women. This is because with women one X-chromosome can cover up the defects of the other, which isnt possible with men.
Also about inheritance, men cannot inherit the xchromosome of their father.

if you go back in time and have sex with yourself is it gay or masturbation

How much weight would you gain if all the hydrogen in your body would be deuterium instead. If you only ate food that contains deuterium, how long would you have to eat that before your body only contains deuterium

>>8639897
This number is more or less our infinite.

>>8640002
>How much weight would you gain if all the hydrogen in your body would be deuterium instead.
Given that we are composed of 70% water, which has 2 Hydrogen.

Hydrogen has a molar mass of 1, Deuterium a molar mass of 2, Oxygen a molar mass of 16.
Which means we've gone from 18 molar mass to 20.

The mass of water in our body is now 20/18 = 1.11 times heavier.

Since water is about 70% of our body, then 0.70% of our body is now 1.11 times heavier, which means 100% of our body is now 1.0777 times heavier.

But that's only for the Hydrogen in water, not counting our carbon components.

>>8640019
That was what I was thinking off. But then I realised I was stupid.

https://en.wikipedia.org/wiki/Composition_of_the_human_body

10% of the body is hydrogen. Taken on a 70kg body. So its a 10% increase in weight.

Not as much as I expected, as I was trying to factor in triglycerides.

Can someone explain how the fuck the Levi Civita symbol works? I can just about maybe understand how

(∇XA) = ϵ_ijk e^i ∂_j A_k

if I write out the entire cross product determinant and check each term, but it isn't intuitive or obvious ot me at all. Now I have to prove the identity

ϵ_ijk * ϵ_klm = ?_il * ?_jm - ?im * ?_jl

and I have no idea where to even begin.

>>8637934
x^(4/3) is locally lipschitz.
By picard lindelöff your solution is unique.
What a stupid problem to practice the picard iteration

>>8639035
someone should edit this into a a pepe

>>8637592
Thinking real hard.

https://www.youtube.com/watch?v=QHanyzP3C6o

At the start of this video, he measures the watts, volts and amps of the circuit with this device plugged in. How is he only getting 0.2 watts when the volts and amps are so high?

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W-what


can a set be a member of itself?

All i get by googling is meme shit about a paradox I just don't know how to answer this

>>8640672
>>can a set be a member of itself?
This is a wellknown problem in mathematics back in the day when set theory was pushed forwards. Because, does a set that contains all sets that contain themselves, contain itself?

But im too bad at maths to tell you whether youre getting trolled or there is an answer to this.

>>8640262
It's equal to 1 for an even permutation of (1,2,3) and -1 for an odd permutation of it. If an entry appears twice or more, it's 0.

>>8640672
clearly A is not a member of itself, is {1,2,4,a,b,c} in {1,2,4,a,b,c}? It's false.

The paradox is:
>>8640687
that's not what's going on here though.

If A \in A is true, then it's possible they made a mistake and meant to say "a" for the element.

>>8640777
>is {1,2,4,a,b,c} in {1,2,4,a,b,c}

it seems like it would be ?


and an empty set is a member of A too, right ?

>>8640784
no, for example

{a} is not in {1,2,4,a,b,c} but a is. {a} is a subset.

the empty set is not a member of A. it's a subset.
if A = {1,2,4,a,b,c,{}} then the empty set would be a member. Make sense?

>>8640791
I think I get you, thanks anon for helping a brainlet.

A isn't a member of itself but a subset of itself, right?

>>8640784
this is a pretty good explanation of the issues surrounding sets that contain themselves:
http://math.stackexchange.com/questions/1046863/how-can-a-set-contain-itself

Based on the axioms (ZFC) that are basically settled on for set theory, A is not in A for any set A.

>>8640797
exactly. It's a subset but not a proper subset.
https://en.wikipedia.org/wiki/Subset

How do you stay focus on your self study when you have graduated and are working full time? Any tips?

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If you flip three fair coins, what is the probability that you'll get a head on the first flip, a tail on the second flip, and another head on the third flip?

I thought it was:

1 - (1/2 * 1/2 * 1/2)

t. Newspaper Idiot

>>8640813
yeah, for any specific sequence it is 1/2*1/2*1/2=1/8

>>8640817
So I was getting the probability but then finding the probability of that not happening. Thanks Anon.

t. Foolish Fool

>>8640825
>>8640813
You don't need to memorize anything, just think logically of what needs to happen.

you need to:
>do something that has a 50% chance
>do something that has a 50% chance
>do something that has a 50% chance

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Is this correct, the bar means complement of A, which is everything that is not A?

>>8640809
weed

I'm not sure if this is the right board. I'm studying Veterinary Medicine and I'm having trouble finding decent anatomy resources.

Got any recs?

Would anyone have any good links to information regarding academic job talks?

>>8640943
yes

>>8641028
If you're going to go on the job market soon, you should talk to your advisor and go to some job talks.

If not, don't worry about it and put your head down and keep working.

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I am reading a book about logic. This section is about first order logic and it has this exercise. I have to prove that statement.

To clarify, T is a theory and P is a formula.

Shouldn't the author specify T is consistent for this problem? If T is allowed to be inconsistent then the theorem is trivially false.

>>8641177
>If T is allowed to be inconsistent then the theorem is trivially false.
why?

>>8641194
Because if T is inconsistent (contains a contradiction) then T U {P} will still contain a contradiction. The ones T has.

3+2=?

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>>8641197
you're probably right, at least that's how another source states the theorem

https://books.google.ca/books?id=AKKOFOcBb2sC&pg=PA15&lpg=PA15&dq=p+is+independent+of+t+if+and+only+if+both+consistent&source=bl&ots=uG8B_7WDk7&sig=76_2L6jXFu-A28UyGLNesUyWz3M&hl=en&sa=X&redir_esc=y#v=onepage&q=p%20is%20independent%20of%20t%20if%20and%20only%20if%20both%20consistent&f=false

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So are Physicists deep down basically just waiting around for the technology to develop to be able to test the predictions of all the TOEs it's already come up with?

>>8641205
Ok, I guess it is just an obvious assumption make then. Or at least the author thinks that.

Now that I'm already asking questions. If Set Theory is a first order theory, and if natural number arithmetic is also a first order theory, how does it make sense to define first order theories in terms of set theory and natural numbers?

>>8641209
Nope, we (theorists) don't give a fuck about testing our predictions

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So, /sci/, it's been a few years since my last math class, and I've totally forgotten some basic shit.

You could walk me through isolating b, step by step?

>>8641375

* Could you

English is my first language. I'm just really tired.

>>8641375
>>8641377

Nevermind, I figured it out.

I swear to fuck, I'm so braindead this semester, and I need to not be.

>>8641375
Multiply both sides with b and 340 and divide both sides by sin45

>>8641365

So on that thread, theorists are already happy that they've got a theory of everything in whatever theory they're backing?

I need to prove that the convex subset:

{x in R^n such that ||x||_p <= 1}
is equal to
the polar set of {x in R^n such that ||x||_q <= 1}
where p and q are greater than 1 and 1/p+1/q=1

I'm stumped, I know I'm supposed to use Holder's inequality, particularly the case when equality holds, but I can't work it out.

>>8641436
I'm not sure I understand your question. But in general, the only thing that theorists care about is mathematical consistency, and, as a bonus, beauty.
Of course I can't speak for every theorist, but my personal philosophy is that as long as a structure is mathematically consistent, then it really does "exist", at least in some Platonic realm sort of way.

>>8641218
You anons are wrong and it's pretty funny because you're making a simple logic mistake when talking about logic.

This property (c) here is a valid definition without having to assume anything about T. It only means that P cannot be independent of T if T is inconsistent (because, as you mentioned, in that case, T U {P} will be inconsistent if T is). It's not a definition that "only works if T is consistent" or something. It's a definition that implies that a formula P cannot be independent of an inconsistent theory. And if you try to think about what independence means in this scenario and how you would go around and define it for an inconsistent theory T, you'll understand why it's defined that way.

>>8641464
What I tried is noting that x is always an element of the polar set, since ||x|| <= 1 implies <x,x> <= 1,
then I let y=zx so <x,y> = z<x,x> <= z
so y = zx where z is in [0,1].
Then by Holder's equality case, <x,y>=||x||_q*||y||_p, but there exists ||x||_q=1, so the set is equivalent to {y in R^n such that ||y||_p <= 1} which is the same as the first set.

I feel this is correct, except I may be jumping the gun by letting y=zx, it feels like I'm missing a step before I can say this must be the truth.

>be me
>transferred from a CC to cal poly pomona for computer engineer
>First semester
>didn't do well and second semester I had to talk to my advisor to remove my advising hold
>Told him that I was gonna change majors and I just needed to remove the hold to register for classes
>He signed a paper to give to some person to remove the hold then told me to get out of his office and stop wasting his time

What do?

>>8641558
he signed a paper that allows you to remove the hold? get the hold removed then?

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Can someone explain this meme?

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i got it right but dont get it

>>8641608
what dont you get?

>>8641608
op: I meant both of them

>>8641609
i don't get any of it, like what is a subset? why does t1 have to be onto and not one-to-one?

>>8641625
you shouldnt be taking linear algebra if you dont know what a subset is

also nowhere does it say T1 has to be onto

>>8641629
"where T1 is onto"
the wrong answer would be "consider T2(x) = -T1(x), where T1 is one-to-one"

>>8641625
This second question is kinda dumb. The last two answers are both valid counterexamples to the statement that you want to disprove. T1 being one-to-one does imply that T1 is onto, meaning that if you can find a T1 that is one-to-one (and therefore onto) for which the statement doesn't apply, you've prove that the statement is wrong.

It's more "to the point" to use the 5th answer than the 4th as your counterexample, but the 4th is still valid, just not optimal.

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>>8641637
>T1 being one-to-one does imply that T1 is onto
??? u wot m8

Are the following two the same or is the second one faster in python:

1) Find a regular expression in a block of text
2) Divide block of text into words. Once you find a regex match within one of the words, exit out

I ask only because I've heard that Python is 'Greedy' with its regex matching

>>8641660
why don't you test it anon and report back?

https://docs.python.org/2/library/timeit.html

>>8641660
Well, dividing the text sounds like 1 pass and then pattern matching sounds like a 2nd pass, so... probably just using the regex would be a lot faster...

How useful is lambda calculus for physics and math?

Is it only trendy because of dumb programmers who think functional programming is the same as mathematics?

How analogous is the math to what someone might use in functional programming?

>>8641708
>>8641661
Tested it and the regex-only was faster (.003 vs .05 seconds) in finding a word in a text file with all permutations of four letters (aaaa, aaab, aaac....zzzz)

im supposed to draw 14 isomorphic graphs with 3 vertices and 3 edges
I can only think of 3
anyone can help me think of the rest?

>>8642594
actually scratch that i got it myself

Why is
>biology
>hard science
a meme?

Small stats question:

(Given that it's an exponential distribution, f(t) = (mean)*e^(-mean * t) )

If mean = 10,000 hours, for what time can we expect the reliability to be .99? (P(Failure) < .01)

I integrated ∫f(t)dt from (0 to x), and solved it for ∫f(t)dt = .01. I eventually got that

X = ln(.99)/-10,000

Did I do something wrong? This seems way too small of a number for an expected lifetime of 10,000 hours

>>8637577
>/lab/
?

>>8642630
It doesn't require much problem-solving. It's mostly just memorization. Statistics is not problem-solving.

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A electric current made up of wood blocks(black) and connect by 2 lines(orange) is suspended and later goes in free fall; in comparison with free fall, the current goes faster when let loose above an horizontal surface, why?

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>>8642843
this exemplifies it better, blue being the horizontal surfance

>>8642843
>electric current made up of wood blocks
wat

>>8637460
OP you saved me

I have a discrete strutures exam tomorrow and there's something I can't figure out:
A+B+C=20 ,how many integer solutions for a,b,c =>0 ?
the way the professor did it was by adding the number of plus signs to the 20
then finding the C(20,2) as in C(n,k)=n!/k!(n-k)!
>please explain the reasoning behind this

A+B+C=10 how many integer solutions =>1
he did it like this:
(A-1)+(B-1)+(C-1)=7
then let (A-1)=X,(b-1)=Y,(C-1)=Z
and then all the sudden it's
X+Y+Z=4
>how did the 7 become 4 ?
please explain this to me I'm out of options
>it's 3 am here

Thanks

>>8642916
>>electric current made up of wood blocks
lol, actually not a electric current but a chain, i'm fucking retarded sorry

>>8642843
posting once again but this time i worded it correctly

A chain mad up of wooden blocks inclined connected by two wires is suspended and then released, compared to free fall, the chain falls faster when it's dropped onto a horizontal surface rather than a inclined one

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not sure where the 2/a factor comes from. also not sure how to work R in. I'm fine deriving the non-driven heat equation but yeah, kinda stuck here.

>>8642961
k got it now

Suppose you have a six sided die. You can put any combination of integers on the faces, as long as it adds up to 21 e.g. 1,2,3,4,5,6 as standard or 3,3,3,4,4,4 or 1,1,1,1,1,16.

If you match these dice against each other in an infinite number of games where the highest roll wins, which is statistically the best?

As an example, if we take the standard 1,2,3,4,5,6 against 1,1,1,1,1,16:

Every combination occurs with equal likelihood, and we have 36 outcomes. There are 5/36 draws (both roll 1), 25/36 wins for standard (and number > 1 against any of the 1s) and 6/36 wins for the non-standard (16 vs any number).

Is there a good way to approach this problem? Can we generalise it somehow and solve? My intuition says that a relatively balanced die like 3,3,3,4,4,4 or the standard 1,2,3,4,5,6 is best; but I am not sure.

>>8643012You need to define "best die" first. The one that wins most tosses against a randomly selected die?
Because no matter which die you choose, one can always construct one that beats it.

>>8643032

I mean, faced in 36 games (so every combination of numbers) against every die it is possible to construct, which one wins the most times.

>>8642923
Think of it as distributing elements in boxes. In the first case, 20 elements into 3 boxes. To separate the boxes, we need 2 separators. Picture it like this
oooooIooooIoooooooooooooooooooo
The number of solutions is now the permutations of this thing, which is (20+2)! (all elements) divided by 2! (The walls are identical) and by 20! (The balls are identical). This is also why your teacher added the number of plus signs.

>>8642945
Does it really?

>>8643071
yes

If the earth completes a full rotation every 24 hours, and it revolves around the sun over the course of a year, then why don't day and night switch places every six months? Wouldn't noon for a place in January be midnight for that same place in June since the sun is now completely on the other side of the earth? I have a learning disability.

>>8643100
Are you really curious or just trying to test us? It falls faster because as soon as one end of the first log hits the surface, it's torque will yank on the wires, accelerating the whole thing towards the ground (asymmetrically, but still). Same goes for all the other logs.

>>8643108

It depends how you define a 'day'. There's a nice article on Wikipedia that explains what you're talking about:

https://en.wikipedia.org/wiki/Sidereal_time

In particular, this picture:

https://en.wikipedia.org/wiki/Sidereal_time#/media/File:Sidereal_Time_en.PNG

>>8643108
I'm bored so I'll just answer any fucked up question in here.
"Day" of course means "facing the sun". In a year, the earth rotates 366.25 times. If we divided the year into 366.25 days then yes, day and night would switch. But we divided it into 365.25, so day stays day stays "facing the sun"

I'm trying to find magazines/monthly journals that relate to physics, so I can delve deeper into my interests. What sources should I read to get started?

>>8643112
thanks

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I don't know shit about Fourier transforms yet but I need to which Fourier transform leads to the bottom right thingy.

I know that the Fourier transform of Cos(x) leads to the top right with 2 symmetric up arrows but I need bottom right with 3 symmetric up arrows

>>8643199
Nevermind, I got a formula for an arbitrary amount of arrows so it's good

>>8637460
ok, I have the area and the ratio of length to width
how to calculate length and width

Starting group theory
Is there a simple example of a geometry in which the isometry group is abelian?

how do i do this?

lim 1/x secx
x->(pi/2)+

specifically how to graph 1/x secx. it's been a year since i've taken trig and i don't remember how to do it

>>8643240
from the examples in
https://en.wikipedia.org/wiki/Isometry_group
the isosceles triangle and the circle

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Why is it 0? Why not 2?

>>8643255
its a typo, it should be 2

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>>8643262
i sincerely hope you're not fucking with me, this assignment is kicking my ass

>>8643265
L2 is defined by a single point and a direction vector

one point is (x,y,z)=(2,-1,0) and another is (x,y,z)=(4,5,4)

so the direction vector goes between these two points, i.e. (4,5,4)-(2,-1,0)=(2,6,4) which is the same direction vector as (1,3,2)

>>8643254
Thanks

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I'm assuming that X can be infinitely dimensional here, and I'm not sure how I would answer it in that case

>>8643296
how would you do it in the finite dimensional case?

>>8643306
If X was finite, my idea would be to use the [math]||x_n - x||_{a,b} < \epsilon[/math] definition of converging to [math]x[/math] and then use equivalence of norms on finite dimensional vector spaces.

I know that this isn't true for general infinite dimensional vector spaces though, so that's probably the wrong idea

>>8643315
you're making your problem too concrete. you need less, not more. for example, you don't need them to be equivalent as norms, or even norms.

spoiler: (((you only need them to be equivalent as hausdorff topologies)))

>>8643254
>circle
Wait, how can that be? Isn't the composition of reflection and rotation not commutative?

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How do i solve this?

>>8643397
factor the top and bottom

>>8643406
and then what? it factors to (x+2)(x-4)/(x-2)(x-3) and i cant cross anything out

>>8643420
you dont have to cross anything out, you should be able to see the limit from that factorization

>>8643427
the limit is supposed to be either positive or negative infinity, how do i tell the difference?

>>8643429
(x+2)(x-4)/(x-2)(x-3)

approaching 2 from the right, (x+2) is positive, (x-4) is negative, (x-2) is positive and (x-3) is negative, so (+)(-)/(+)(-) gives you +infinity

I am working on a python programming project and normally I can search my way to an answer but in this case I'm unsure what the right terminology is, something about confidence intervals?

I am interested in finding out how probable a streak of consecutive increases is to continue. I have my sample data broken to look something like
Streaks of 5 there 122 occurances
Streaks of 6 there 67 occurances
Streaks of 7 there 30 occurances
Streaks of 8 there 13 occurances
Streaks of 9 there 11 occurances
Streaks of 10 there 9 occurances
Streaks of 12 there 1 occurances
Streaks of 14 there 1 occurances
Total of 254 streaks

What do I need to do to compute the likelihood that a streak of 5 is to continue to 6, 6 to 7, etc... I realize that this is just a sample so the data and things like if the distribution are normal come into play. What approaches are there that I can implement to find a solution?

>>8643636
Out of 254 streaks, 122 didn't continue past 5. The probability of a 5-streak to continue is 1-122/254.
The prob of a 6-streak to continue is1-67/(254-122) etc

I'm sure this is obvious for anyone with knowledge in physics but that isn't me and I haven't found anything online

To me there seems to be an incoherence in Einstein's relativity formula

as follows:
t'=t/sqrt(1-v^2/c^2)

Where t' is the time the movement takes for the observer and t the time it takes for the subject in movement
It makes sense, but when v tends towards c

lim(v=>c)t'=infinity
So it takes an infinite amount of time to observe a movement that is finite for the thing moving?


But if t is finite (which let's say it is in this situation) and t' is supposedly infinite, wouldn't v also need to be infinite?
Does this mean the formula is not applicable when the speed is equal to the speed of light?


I'm explaining this very badly but I hope someone understands what I'm trying to say

>>8643725
What you're grasping at is if you're moving at c, time stops for you.
Hence forward "time travel" by moving in a circle at c.
This same argument can be continued to show that if you move faster than c, you move backwards in time and can violate causality. (I mean, you can't, because you can't move faster than c, but you get the point)

>>8643747
so does this imply that from a photon's perspective, time around it has completely stopped?
if that's the case, how is it possible for us to see light, since wouldn't it go past us without us being able to perceive it?
also if time stops, how is it possible for anyone to observe it?

>>8643725
>>8643747

>Does this mean the formula is not applicable when the speed is equal to the speed of light?

Yes, there is no inertial frame moving at the speed of light relative to some other inertial frame that can be reached via Lorentz transformations.

>>8643755

Light does not have an inertial frame we can go to--we can't discuss 'what the photon sees' since there's not a frame following the photon I can attach myself onto.

Everyone who's massive--let's restrict ourselves to the flat space case or at least local measurements--is restricted to a class of inertial frames all not moving at the speed of light relative to one another. Massless particles are necessarily moving at the speed of light, and this measurement is universal within any intertial frame (everyone with mass sees them traveling at the speed of light, though perhaps with different direction).

>>8643755
time in it's inertial reference frame, sure. It would be very confusing to be a photon! It's entire life would appear instantaneous to itself.

That doesn't mean in all reference frames. We see it just as we should, as something moving at c relative to us.

>>8643759
>>8643762
so, if I've understood, light always travels at c for us as we observe it

but relative to us time doesn't move on for a photon like it does with us?

>>8643651
Thanks anon this is something I can implement. Also to advance the question - there must be some probability that a streak will continue past the current max, how would I estimate that chance?

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can anyone help me interpret this question? as far as I can make out, the wavefunction is spherically symmetric, so it doesn't matter what component of angular momentum is measured. In fact, are all components just zero?

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Key says B, but wouldn't it be A because the fluid would have the highest velocity at that location? (Assuming laminar flow)

Why does the snow on the roads turn brown? Its not from sand

>>8644297
> In a steady flow of an inviscid fluid without external forces, the center of curvature of the streamline lies in the direction of decreasing radial pressure.
https://en.wikipedia.org/wiki/Euler_equations_(fluid_dynamics)#Streamline_curvature_theorem

>>8644119
You don't have any evidence yet, so you can only extrapolate.
There are many different ways of extrapolating (for example 2 streak - 16 occurences, 3 streak - 8 occ, 4 streak - 4 occ => by extrapolation 5 streak should have 2 occurences since they seem to follow the pattern of n-streak - 2^(6-n) occurences.
The easiest way to extrapolate would be by polynomial extrapolation

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Alright apparently I'm fucking retarded. I don't see why pic related is equal to x^(x-1). It seems to me that this should be 1^x. Please break this down Barney style to me. Thanks.

>>8644543
(x^x)(1/x)=(x^x)(x^{-1})=x^{x-1}

>>8644543
Because the term on the right is x^(-1)

>>8644553
Got it thanks. Brain fart apparently.

>>8644543
>>8644560

Yeah you are retarded. You should get that checked out.

Please help me with this one.
I have full-size headphones (beyerdynamic dt880) plugged into an external USB DAC that is on my desk.
Whenever I stand up from the chair and lift my leg up, the DAC stops working and status LED turns red, also the metal parts of the chair sometimes give me static shocks when doing so.
What damage may I be causing to the aforementioned electronical components by doing that, if any?
The PC is on the floor near me. The floor and the desk are wooden.

>>8637460
What is the furthest the hands on the DOOMSDAY CLOCK and be from midnight?
is it always minutes to midnight or could in some surreal period of nukelessness be like 4pm?

How would I show that:

[math]\frac{3}{7x-4}=\frac{1}{1+\frac{7}{3}(x-1)}[/math]

Its making me feel absolutely retarded, but I just cant figure it out.

>>8644929

[math]\frac{3}{7x-4} = \frac{1}{\frac{1}{3}}\frac{1}{7x-7+3}=\frac{1}{1+\frac{7}{3}(x-1)}[/math]

There you go anon. In general, remember that you can always add and substract or multiply and divide by the same quantity without problems, and that can sometimes be really helpful to simplify a problem (some rational integral are done using this technique, for example).

>>8642746
laboratory
surely all these people that ignored my post understood what I mean't, r-right?

>>8644929
Multiply top and bottom by 1/3

>>8645001
>>8644929

[eqn]\frac{3}{7x-4} = \frac{1}{\frac{1}{3}}\frac{1}{7x-7+3}=\frac{1}{1+\frac{7}{3}(x-1)}[/eqn]

Sorry, this should work.

>>8645008

The 4chan TeX previewer is a bunch of bullshit.

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Is it technically correct to say that "time" is the moving force of the universe, or is there a better term I should be using?

>>8645291
> moving force
you should use the term gravity as it's an actual force.
Although at intergalactic scales, some weird force is happening.

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is the limit of -6 from the left in this graph 3 or does not exist or what?

>>8645468
doesnt exist

>>8645471
cool thanks

For high enough velocities, can the interstellar medium be treated as air, meaning can we use aerodynamics formulas to approximate the behavior of objects?

When a photon reflects off of something, is it the same photon?

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How do I start going about solving this D.E.? Every route I take seems to fail but I know I am forgetting something dumb.

>>8637460
Is it possible for two spaces to fail to be isomorphic even if all their topological properties coincide?

>>8646637
Isomorphism of topologies is a topological property. You might want to reevaluate what you mean by "all their topological properties"

Or maybe you mean isormophic as something else? The closest example is metric spaces. Two metric spaces, one complete and one not, can be homeomorphic

hey /sci/, stupid question, but how can I solve this Sum for n other than simple trial and error for a given result z?

[math]\frac{32}{2} \sum_{k=1}^{n-1} \frac{1}{k} = z[/math]

>>8646724
not easily
https://en.wikipedia.org/wiki/Harmonic_number

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Does this look right?

>>8646672
My mistake I'd mis-remembered something.

>>8646735

Oh hell, no wonder I didn't succeed

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>humanity can zoom into galaxies thousand of light years away
>There is no zoom image of the reflectors on moon
And people believe we went on the moon

>>8646957
You can't resolve something that small.

>>8639897
Multiply by 0 on both sides and you'll get 1=0. That's where division by 0 is underfined.

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Can anyone help me find out what's wrong with this proof?

Like obviously this isn't true and I could disprove it with an example, but I need to figure out what's specifically wrong with the induction.

>>8647170
"if n+1 is prime then the inductive hypothesis doesn't give you log15(p)+log15(q)=log251(p)+log251(q) since one of p and q is n+1"

help:

for any two arbitrary norm, ||.|| and ||.||', show that there exist a,bER such that a||.|| <= ||.||' <= b||.||

>>8647185

also, any sequence {x_1,...,x_d} in R^d satisfies a property B iif each x_n satisfies property R

because all i've seen so far in introduction to topology is applying R to each R^d

>>8647182
>>8647179
So it kinda goes into an infinite loop? Like it wants to find say... log(13), so it turns that into log(1) and log(13), but then it needs to solve log(13) so it goes back and repeats?

how to solve

y''+4y'+4y=t^2*e^(-2t) when y(0)=0 and y'(0)=0

with laplace transformations?

>>8647207
yep

>>8647211
>nvm i think i got it now

Why would I ever need anything beyond basic arithmetic in the real world?

>>8647387
>Going for a walk outside
>Suddenly kidnapped
>Told to prove the Poincare conjecture or I will be killed
>Never took Ricci Flow 101 b/c I was a normie and just needed basic arithmetic
>i die

>>8647182
not him but what if you have
[math]\log_{15} k =\log_{215} k \text{ for all composite } k+1\,.[/math] why is that not true?
is the step [math]\log_{15}p+\log_{15}q=\log_{215} p+\log_{215} q[/math] also incorrect?

>>8647463
only having it for composite numbers is weaker than having it for all naturals, so the inductive hypothesis still can't be used

>>8647463
Because numbers don't factor into composites. They factor into primes. If you had it for only primes you would be fine, but you can't even prove it for k = 2.
how are you supposed to break up 34 into a pair of composite numbers so you can induct

>>8647387
If you don't want to do any kind of science, engineering, operations research, or market analysis, then yes, you can get by in life being uneducated.

Is there any significance, in relativity, to the number [math] \sqrt{1-\frac{1}{2gx}} [/math], or, putting back the c2, [math] c\; \sqrt{1-\frac{c^{2}}{2gx}} [/math] where g is some acceleration?

I was playing with equations trying to find out how lorentz transformations behave when under constant acceleration in a straight line and came to this expression along the way, but that doesn't make a lot of sense because what the fuck would happen when x<=1/2g??

>>8647484
Even if I do those things can't I just use a calculator though?

>>8647520
mgx is the work/energy you need to push the mass m along a distance, against the constrant force F=mg.

mc^2 is the energy associated with the mass as such.

what were you even computing?

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Question on group theory. Need help with the second question. Prefer hint over a solution.

Can I safely make a sand bath for a small pear shaped flask by simply packing it into a 250ml beaker and heating with a flame? Or does the sand bath need to be bigger, and heated in another way?

>>8647535
pick a generator for the group and suppose the order isn't prime, get contradiction

>>8647539
fuark I'm retarded

thanks homie <3

>>8647535
|G| is prime comes from Lagrange's Theorem. If you understand the theorem then the second part should come immediately.

Is pornography science?

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The wording has confused me more than anything, can someone explain?

>>8647552
what are you confused by? the bijection is just
a <-> (a,f(a))

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>>8647532
Now that you mention, I guess I forgot to put the mass in my equations. What the hell, they all weight one [unit] anyway. I was computing, as I said, stuff about constant acceleration. The formula I wrote back there is what I got out of a very convoluted calculation for the velocity of a body under constant acceleration parametrized by his position instead of time. It was the first result I got and the result is not that bad, it has asymptotes at v=c or 1, but it is imaginary when x<1/2g, so maybe if I just shift it to the left a bit it will be okay.

>>8647549
>|G| is prime comes from Lagrange's Theorem.
how so?

What I've figured out:
Every piecewise monotonic function must end in either the largest or the smallest # in a set

The number of sequences that exists that follow the above rule are n! - 2(n-1)!

I know the answer is 2^(n-1) because I manually calculated {1,2,3,4,5}

But there's some link between the size of the set and the # of valid permutations I can't find.

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>>8647620
Forgot this

So this question isn't technical in nature, but I wasn't really sure where else to ask.

I'm a 2nd year undergrduate and I'm taking a graduate-level course on algebraic number theory. I'm able to follow along in the lectures pretty well and have no difficulty understanding the material.

When it comes to problem sets though I've been struggling really hard. Is this typical of graduate classes? Am I not expected to be able to reasonably solve all of the assigned problems without resorting to looking them up?

How long do you think it will be before they can reliably chop off someone's head and put it onto a new body and have it all work without complications?

I know some guy is talking about doing it soon but I mean about as reliable and safe as other major surgeries someone could have, like a heart transplant or something.

>>8643772
All we can say is, for anything moving at the speed of light, our equations say that it ceases to experience time. It's probably hard to quantify what that actually "means" for a photon. It obviously doesn't mean that it ceases interaction with time-experiencing things. Photons are strange things.

>>8645291
define "moving force" more clearly and you'll probably find your own answer.

>>8647688
>body transplant
I feel like they'll be able to regenerate your current body with CRISPR before they can do that

We're looking at shapes, described by NURBS curves (non-rational uniformal B-splines) and know all control points. Therefore, we know all points on the perimeter of the shape. It is given that the boundary is closed, and does not cross itself.
We are looking to describe the local connectivity value(lcv) of each point on the curve. Numerically, you would attempt to solve this by taking a set number of points, let's say 1001, and interconnect all of them. connection lines that lay outside the shape (partially or whole) are invalid. You then look at each point on the perimeter and see to how many points it can connect under this condition. The number of all valid connections of a point divided by the total number of other points (in this case 1000) is the lcv of a point.
Looking along the perimeter, you then write all points' lcv's in a diagram (x-axis: t (position on perimeter), y-axis: lcv) and attempt to approximate a function for that graph, or intervals of it.
You can now increase the number of measuring points, thus getting a more accurate graph for the t - lcv representation.
While increasing detail in many iterations, I believe you could see how the parameters of the function/s describing the graph would converge towards certain values, which you could use to make a function that accurately puts out the lcv for any point on the perimeter, not just an approximation.

Now, if the parameters do converge, there should be a way to get the final function/s by just looking at the control points of the NURBS' describing the boundary.

My question is: can you say whether the values do converge for any set of curves meeting the conditions mentioned earlier? And if they do, how would you attempt to construct an algorithm that takes one partial curve, and all curves of the shape (including the one we're looking at), that puts out an accurate function lcv(t)?

>>8647687
You are expected to solve most to all of them, in my experience. You are not expected to be able to sit down with 2 hours and a case of beer and do your problem set like you can in undergrad linear algebra; it's quite usual to have to spend several days thinking about problems and trying stuff before you figure out something that works.

If you are spending that much time on them and still don't get it you can probably chalk it up to one of two things; either you're too inexperienced to handle the course (which is a bit harsh, but a real possibility) or you're learning the proofs but not grasping why these results/steps are intuitive things to try. Remember somebody did invent all this without checking a solution manual; they (usually) had a better reason than just writing out random shit until they got something.

Hey guys, social retard here 19 years old, I have a bro that's 16 and he is struggling with his grade 10 pre calc.

He's home schooled so he does it all himself

Any material I can give him or motivation to do good? He's home schooled so he does it all himself

>>8647529
no

>>8648114
Why not? With stuff like Wolfram there's really no reason to learn all these complicated rules and stuff

If I have a function [math]f:R\subset\mathbb{R}^n\to\mathbb{R}[/math] Defined over a rectangle such that [math]f(x)=0 \forall x\in int(R)[/math] then how do I show that the the function is integrable and that the integral is 0? I can only use the definition of integral and the cauchy criterion for integrability (plus obviously other basic properties). I tried partitining the rectangle as [math]P=\{a_{1}, a_{1}+\epsilon, b_{1}-\epsilon, b_{1}\}\times ...\times \{a_{n}, a_{n}+\epsilon, b_{n}-\epsilon, b_{n}\}[/math] with [math]a_{i}, b_{i}[/math] being the points defining the rectangle. However, I'm not visualizing which sections of the subrectangles are touching the frontier of the rectangle and whic are in the interior.

>>8648174
The function is bounded for all you autists.

>>8648174
are you talking about the riemann integral?

>>8648261
Yea, well darboux (inferior and superior sums)

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How do i make the qt in my chem class my girlfriend I have never approached a woman before

>>8648290

Do the opposite of what you normally do.

> I have never approached a woman before

Therefore, approach a woman

How do i solve this?

Let P be the only predicate constant that is unary, and I an interpreta-
tion such that the universe is the set of all university students. For any ξ ∈ |I|,
P^I (ξ) = t iff ξ has taken CSE 579. Represent the following statement in
first-order logic:
(i)There exists at most one student who has taken CSE 579.

How do i represent the condition 'at most'?

>>8648301
But what if I fuck up because I sperg?

>>8648303
i have no idea what most of the words you used mean but maybe think of it like injectivity

i.e. something like P^I(xi_1)=P^I(xi_2)=t => xi_1=xi_2

>>8648314
for the purposes of the person who asked the question then, it is to be phrased:

[math](\forall x) (\forall y) (P^I(x) \land P^I(y) \Rightarrow x = y) [/math]

Since it doesn't make sense to say P(x) = P(y), as P is a predicate, not a function.

Now even then, it depends on the framework of logic the questioner is asking from, if he is working in FOL with equality, then the formulation I gave is valid, otherwise with a vanilla FOL, a different formulation is required (I'll have a go at thinking of one)

>>8648689
...cont

Well an easy way to do this is to simply transplant equality into the statement using an additional equality predicate, so:

[math]((\forall x) E(x,x)) \land ((\forall x)(\forall y) E(x,y) \Rightarrow E(y,x)) \land ((forall x)(\forall y)(\forall z) E(x,y) \land E(y,z) \Rightarrow E(x,z)) \land ((\forall x)(\forall y) P^I(x) \land P^I(y) \Rightarrow E(x,y)) [/math]

But this seems like a bit of a tedious solution if indeed you do not allow the equality symbol in your FOL

>>8648306
Just practice

>>8641581
Don't know, but it's made up stuff.
It's Opipramol and Fluvoxamine joined together.

>>8647622
2?

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with a high school understanding of foundational topics:
could i teach myself circuit design with 30 hours per week?
what do i read/work on?

>>8650224
possibly, what exactly do you want to learn or do?

I'd say you should start out with
https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/