/sqt/ - Stupid Questions Thread: Saturday Night Edition

>>8907467
How about top 3 things to consider when approaching quadratic inequalities + ?

Are all big stars red giants? What are some of the bigger ones that haven't gone through that phase?

So I decided to read A Transition To Advanced Mathematics. The fact that there are no answers to all the exercises is making me go crazy. I'm answering most of them but I'm definitely not sure whether they are correct. Are there full solutions to this shit?

When some consistent method is used to assign a value to a divergent infinite series, is that the "true" value of that series? In the sense that using other consistent methods in other context on the same series will produce the same value; if you have some series S that occurs when you input an argument x into a function f1, and that same series occurs when you input a different argument y into a different function f2, does the divergent series get the same value when you use mathemagics to assign it one?

>0-9
>10-19
>20-29

in statistics, if you have these classes, clearly the class width is 10. are there still idiots ITT who think the class width is 9?

>https://www.mathway.com/examples/statistics/frequency-distribution/finding-the-class-width?id=1000

>>8908395
Should just go through a standard algebra/real analysis course, but aite. What version of the book are you using?

>>8908496
7th edition

>pirate textbook
>use on demand printing service to publish one off
>now have physical textbook for much less money
Eh? I figure they might not print something that I don't have the rights to but what if I could find a dodgy printing company in the FSU or something? I can't stand all these .pdfs and ebooks.

What is the most fundamental prerequisite knowledge I have before entering an introductory engineering course? I'm talking bone basic, bottom of the barrel, introductory engineering. I know math essentially up to the calculus level but have next to no knowledge of physics, science, or machines. Am I fucked?

>prove the uniqueness of zero

x+0=x
y+0'=y

so, x+y+0+0' = x+y
0+0' = (x-x)+(y-y)
0+0' = 0+0'
(0-0) = (0'-0')
0=0'

is this a sufficient enough proof?

>>8908540
>FSU
Former Soviet Union?

>>8908623
>0+0' = 0+0'
>(0-0) = (0'-0')
i dont get how you got from the first step to the second.
also 0=0'+0=0 is surely a sufficient proof, which i think youve implicitly used anyway

>>8908661
one of those zeros on the end shouldve had a ' btw

>>8908623
Wouldn't it be easier to just say
0 + 0' = 0 (since 0' is an identity element)
0 + 0' = 0' (since 0 is an identity element)
Therefore 0 = 0'
?
Unless you're working in a less obvious context. Do you have commutitivity?

>>8908661

shit, i don't think i know either

>>8908665

theses are exercises of proof showing how the real number system is a field, commutativity is allowed.

In Finite State Automata and regular languages, how does the pumping lemma work?
E.g. to show that not all context-free languages are regular too.

[math]L = {0^n, 1^n | n ≥ 0}[/math]
is not regular. How does the pumping lemma prove that?

Didn't realize I should just post this here:
>>8908907

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how do i find the inverse of pic related without using the adjoint matrix?
i can work it out pretty much by inspection, but i know theres a quick way to do it that involves elementary matrices or something, which i cant remember

>>8908987
you just put the identity matrix beside it
i.e.

5 0 5 1 0 0
0 5 0 0 1 0
0 0 5 0 0 1

and put it into row reduced echelon form, the right half will then be the inverse

>>8908987
In your case it would be dice:
1) Divide first row by 5
2) Divide second row by 5
3) Divide third row by 5
4) substraict third row from first row

That gives the elementary matrices
[math] E_1 = \left( \begin{array}{ccc}
\frac{1}{5} & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \end{array} \right)
E_2 =\left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & \frac{1}{5} & 0 \\
0 & 0 & 1 \end{array} \right)
E_3 = \left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & \frac{1}{5} \end{array} \right)
E_4 = \left( \begin{array}{ccc}
1 & 0 & -1 \\
0 & 1 & 0 \\
0 & 0 & 1 \end{array} \right) [/math]
Then the inverse is [math] E_4 E_3 E_2 E_1 [/math]

That said, the method via the adjoint matrix scales so much better. In here the method of elementary matrices is faster because you get mostly a bunch of diagonal matrices which are piss easy to multiply, but in the real world matrices are not this nice. On the other hand, determinants are always really easy to compute, which is why the method via the adjoint matrix is the easiest and fastest.

>>8908991
That's called the method via elementary row operations. Not the same thing.

>>8909007
elementary row operations are just multiplying by elementary matrices tho

>>8909010
Well, both methods are the same in idea but different in execution.

In the method of elementary row operations, as you did, you have to step by step apply row operations to both your matrix, and your identity matrix. For some this is messy which is why they prefer doing the row operations only for the matrix you are working for and then after the fact, composing all those operations via matrix multiplication.

That said, both these methods are shit because they involve row operations and/or matrix multiplication, which are both very fucking tedious. On the other hand, calculating determinants is really fucking easy.

Adjoint matrix method for fucking life and I will bust a cap in your ass if I ever see you niggas on these streets finding inverses via elementary row operations.

>>8909017
>Adjoint matrix method for fucking life and I will bust a cap in your ass if I ever see you niggas on these streets finding inverses via elementary row operations.
cringe

Is there a complete series of intro real analysis lecture videos freely available on the internet where the audio and video aren't shit and the professor has an intelligible accent?

>https://www.youtube.com/playlist?list=PL0E754696F72137EC
incomplete, doesn't even get into integration

>https://www.youtube.com/playlist?list=PLmU0FIlJY-MngWPhBDUPelVV3GhDw_mJu
shit audio, but might use if no other options

>https://www.youtube.com/playlist?list=PLbMVogVj5nJSxFihV-ec4A3z_FOGPRCo-
shitty accent, can barely even understand when he says a word like "interval", which is unfortunate since it seems pretty comprehensive

>https://www.youtube.com/playlist?list=PLcR4No3nvxFDg6VfaO8paSOv4ClAlyzon
again, doesn't get to integration

>>8907467
>Stupid questions
>305
I got one, why that number?

>>8909143
because the bump limit is 310 and he's a cancerous fag who forces his /sqt/ threads with "math oracle" images so he has to post before the bump limit but not so soon that the mods have time to react

https://warosu.org/sci/?task=search2&ghost=yes&search_text=&search_subject=sqt&search_username=&search_tripcode=&search_email=&search_filename=&search_datefrom=&search_dateto=&search_op=op&search_del=dontcare&search_int=dontcare&search_ord=new&search_capcode=all&search_res=op

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>>8909167
I wrote 305 because I thought it was 305, not because of any 'forcing' or trying to dodge mods lmao, i'm also not the only person who posts with these images

take a break from the internet m8

>>8909181
those pictures are shit and of reddit, which is where you should go back to

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>>8909187
I've never used reddit, what's good over there that I should check out?

>>8909196
r/The_Donald

>>8909196
lots of great stuff, it's way better htan 4chan. you should go there and never post here again

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>>8909200
>lots of great stuff, it's way better htan 4chan. you should go there and never post here again
well that was'nt very convincing

i think i'll stay here

>>8909167
>because the bump limit is 310 and he's a cancerous fag who forces his /sqt/ threads with "math oracle" images so he has to post before the bump limit but not so soon that the mods have time to react
you know people have been posting those images for over a year now right? are you new?

>>8909210
as far as /sqt goes i'm seeing one from june 2016 and then a incessant image forcing from april 12 2017

>https://warosu.org/sci/?task=search2&ghost=yes&search_text=&search_subject=sqt&search_username=&search_tripcode=&search_email=&search_filename=&search_datefrom=&search_dateto=&search_op=op&search_del=dontcare&search_int=dontcare&search_ord=new&search_capcode=all&search_res=op

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>>8909217
lul if you weren't so new you'd remember him from math generals and wouldn't have to look in the archive

https://warosu.org/sci/thread/7909437
>march 2016

chill out with the imageboard policing, go do something better with you're time

>>8909228
that pic was only posted 8 times, https://warosu.org/sci/image/OcfeIyiFVJpJ-xP60RydZA

now fuck offfff

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>>8909240
and all 8 of those posts are more high quality than your whining

imageboard policing doesn't look good on you

>>8909228
>forces obscure shitmeme
>lol u dont know this meme lol newfag

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>>8909249
>multiple people posting several different images of some guy for over a year
>""forcing a meme""
there has to be some image at the top brainlet, what would you prefer?

Is denoting the roots of the 2nd order polynomial as "m" a convention like x for unknowns, i for indices, etc. and where does it come from? Saw it throughout school in textbooks in my native lang, now saw it in an English textbook too

>>8909438
>>8909438
>Is denoting the roots of the 2nd order polynomial as "m" a convention
no

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>>8909041
I get it man, fucking indian accent.

>>8907467
Let S be the set of all integers and define a~b iff a-b is divisible by 3. How many equivalence classes are there?

>>8909992
this is trivial and takes like 1 minute if you just start writing out what's in each equivalence class, where did you even get stuck?

I have

F(x) = 0 if x<=0;
x^2 / 4 if 0<x<=2;
1 if x>2;

I'm supposed to find the DX or variance, from what I read it's supposed to be
DX = E(X^2) - (EX)^2 and
EX = integral(x*x^2 / 4) from 2 to 0, = 1
E(X^2) = integral(x^2*x^2 / 4) from 2 to 0 I get 9/5
So DX = 9/5 - 1 = 4/5, but the textbook says the answer should be 2/9, wtf am I doing wrong

>>8910000
Literally first problem. Am brainlet and am confused as to what im doing. I checked first to see if ~ was indeed an equivalence relation and it is but I have no idea on how to proceed.

>>8910006
do it with 1 and 2 first, then do it for 3

>>8907467
are calculus labs mostly optional?

>>8910012
Im sorry but Im still rather confused. Here is how I am interpreting this: the equivalence relation ~ is denoting when a and b will satisfy the condition a-b is divisible by 3. But shouldnt there be infinite such pairs of a and b that satisfy this condition? Ive set a and b to 1 and 2 and 3 but I doubt thats what you meant for me to try.

>>8909992
it might help to notice that [math] 3|a-b\leftrightarrow a\equiv b\!\mod 3 [/math]. so the equivalence class of some x is [math] [x]_{\sim}=\{b\in\mathbb{Z}:x\equiv b\!\mod 3\}
[/math]. if you cant see how many there are by inspection just try some values of x and eventually youll will

is there a brainlet explanation of spherical harmonics? and how they are used in computer graphics for encoding ambient lighting?

Recommendations for graph theory books on libgen? Just took an intro discrete math course and we scratched the surface of it.

>>8910001
>E(X^2) = integral(x^2*x^2 / 4)

Shouldn't it be E(X^2) = integral(x^2*x^4 / 4) ?

>>8910001
>>8910288

Well it turns out I was fucking up, the textbook has
EX=integral(x*f(x))
and
DX = integral((x-EX)^2 * f(x))
Plugging that shit in gives me 4/15, which was actually my first result I don't know how I fucked up what was in my first post, regardless it still can't be right since the exam practice one has 2/9 set as an answer

>>8910299
Nevermind I figured it out where I went wrong
Apparently I was supposed to transform the x^2/4 and tkae the derivative so it would be x/2, then it worked

How can I orthonormalize a 5x5 without kms'ing?

If Φ(0, 25)=0.5987
Then how do you get Φ^-1(0, 25) =-0.67 and Φ^-1(0, 75)=0.67
Probability distrubition function I think

>>8907467
What does an event having a probability of 0 mean? Can events with probability 0 happen?

>>8910481
roll two dice

the probability of the dice adding up to 1 is 0

>>8910481
>What does an event having a probability of 0 mean?

That it can't happen

>>8910481
Imagine you have a dartboard, and pick a single point on it. What is the probability you'll hit that point when you throw a dart at the board?

>>8910510
there are infinitely many points, but the probability is non-zero. therefore, 0.999... =/= 1

>>8910510
Define point. What I was if I had a bag filled with all the natural numbers what's the probability I draw [some specific natural] seems like it should be zero. However, when I draw one and it turns out to be 7 was my original assumption wrong?

>>8910531
It just shows you there's a difference between saying something has zero probability and saying something can't happen.

>>8910544
if you want to dogmatically assume that 0.999... is exactly the same mathematical 'entity' as 1 then sure

>>8910557
There's theory behind it.

>>8910557
How would you assign probability to these events >>8910531 >>8910510

>>8910559
in the dartboard example you can get very close to zero probability by repeatedly subdividing the dartboard, but you can never reach zero. the limit is zero, but the probability itself is non-zero, unless you have a retarded definition of zero like with the class width bait.

>>8910563
see >>8910564

>>8910564
>but the probability itself is non-zero

Why?

>>8910569
because if i pick a point for example (0.12, 1.90), no matter how unlikely it is, the dart will land somewhere, and (0.12, 1.90) is a possibility

>>8910572
Why does the probability of hitting (0.12, 1.90) is nonzero?

And if it's not zero, then what is it?

>>8910572
you're wrong, just because it's a possibility doesn't mean it has non-zero probability

if i ask you to guess the natural number i picked out between 1 and n, the probability you get it right is 1/n, which tends to zero as n goes to infinity, so the probability of you guessing right when i choose from all natural numbers is 0.

>>8910581
*does that mean

>>8910581
because if you use a definition of probability which isn't pants on head retarded, a zero probability means it's impossible, but hitting (0.12, 1.90) is possible, so the probability is 1-0.999...

>>8910588
>statfags being retarded again
next you'll say that the class width is 9 or 9.7 or some bullshit >>8908491

>>8910596
what does class width have to do with anything here?

>>8910588
Not the guy you replied to. So how do we make sense of events with 0 probability occurring?

>>8910601
>>8910601
>So how do we make sense of events with 0 probability occurring?
define 'make sense of', what are you confused by?

>>8910596
Go away.

>>8910596
>>8910596
>next you'll say that the class width is 9 or 9.7 or some bullshit >>8908491
but that class width is 9, max - min of any interval is 9

>>8910596
>the probability is 1-0.999...

What is the probability the dart lands on (0.12, 1.90) or it lands on (0.13, 1.90)?

>>8910607
shitty bait. just look at

https://www.mathway.com/examples/statistics/frequency-distribution/finding-the-class-width?id=1000
>The class width is the difference between the upper or lower class limits of consecutive classes. All classes should have the same class width. In this case, class width equals to the difference between the lower limits of the first two classes.

http://tistats.com/definitions/class-width/
>Class Width can be calculated by:
>Difference between two consecutive lower class limits
>Difference between two consecutive upper class limits

if you have an image of width 10 and you number the pixels from 0 to 9, the width is still 10, fucking faggot

>>8910610
2(1-0.999...)

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>>8910612

>>8910614
KILL YOURSELF

>>8910603
what does it mean for an event to have probability 0?

>>8910601
See >>8910544

Zero probability events are said to happen "almost never."

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>>8910614

>>8910617
not an arguement

>>8910613
What is the probability the dart lands on any point of the form (x, 1.90)?

>>8910620
the probability of rolling 1 with 2 dice is "literally never", so since you can't distinguish between these cases it seems you have a pretty retarded definition of zero probability

>>8910620
Ok. I'll Alta Vista this term.

>>8910635
literally never is a subset of almost never

go take a probability class moron, your freshman intuition is wrong and you should stick with mastering the quotient rule for now

>>8910635
What's the difference in the conditions that makes you think you have a point?

>>8910642
kys this is as fucking stupid as the width bullshit

>>8910618
An event has probability zero if, roughly speaking, the size of the event is zero compared to the size of the whole space.
When an event _never_ happens, the set of viable events is empty, so of course it has no size.
But for something like hitting one point on an (infinitely divisible) dartboard, even though it's possible to hit this point, a point has no area in two dimensions, so the probability is still 0.

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>>8910614

>>8910649
https://en.wikipedia.org/wiki/Psychological_projection

fucking retarded statfag

>>8910648
Thank you. This is clearly explained

>>8910614
>this is what brainlets actually believe

>>8910614
(You)

>tfw you fell for the max-min meme

>>8910670
>not an argument 2: electric boogaloo

>>8910614
This needs to be a bannable offense.

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>>8910654
>>8910670
>>8910672
https://en.wikipedia.org/wiki/Autism

Why does integration by parts work?
I know it's found by taking the antiderivative of the product rule, but I want to find the integral of u*v and the formula is for u*dv. So if I want to integrate e^x * sin x, IBP forma gives me integral of e^x cos x = ...

Why does this work when the left side is a completely different value?

>>8910700
t. retarded statfag who can't read

>The class width is the difference between the upper or lower class limits of consecutive classes.

>>8910717
go read a book freshman

>>8910720
lol, you can't even recognize how retarded your statfag shitbook is, you just take everything at face value from your (((professors)))

>>8910720
and you're probably reading your book wrong and it doesn't even say your retarded shit definition of class width

>>8910720
>Using freshman as an insult

How is the summer before your sophomore year doing? How big was the dildo you licked Milwalkee's Best off of at your Kappa Epsilon Kappa pledge ceremony?

>>8910756
degree in being retarded

>>8910764
>degree in mathematics education grades K-3

>>8910764
>7
>8
>9
zero width according to you

>>8910739
That is a rather specific scenario to be imagined

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>>8910765
pure math actually :)

>>8910767
[math] \int_7^7 dx = 0 [/math]

>>8910772
[math]\int_6.5^7.5 dx = 1[/math]

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>>8910785

>>8910772
I didn't realize devry offered such courses

>>8910788
KILL YOURSELF

you're clearly just trying to bait and waste poeple's time

the point is that anything between 6.5 and 7.5 goes into 7 and the width is 1

http://mathworld.wolfram.com/ClassBoundaries.html

YOU'RE OBJECTIVELY WRONG FUCKING MORON

>>8910772
>pure math actually :)

You have 5 minutes to show that the factor group Q/Z isn't cyclic; for theorems on cylic groups, you're only allowed to use that cyclic groups of the same order are isomorphic. You have an additional 5 minutes to show that the Cantor set is perfect. Original solutions, only. You should be able to solve this.

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Final in intro probability tomorrow night. Need a concise textbook recommendation for me to power through. I already know like 60% of what we're gonna cover, but have no text for reference.

Does anyone know any place to find comprehensive tests or something similar for math courses?

>>8910834
google coursename final exam year_xa year_xb year_xc currentyear

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>>8910793
>devry
literally who?

>>8910800
pic related

>>8910858
>literally who?
take your own advice and read a book some time kid

>pic related
haha very funny here's your (You)

go ahead and contact stephen wolfram to make a correction according to your shitty unsourced definition

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>>8910871
>take your own advice and read a book some time kid
what's a good book about devry?

>go ahead and contact stephen wolfram to make a correction according to your shitty unsourced definition
what does wolfram have to do with this?

>>8910876
http://mathworld.wolfram.com/ClassBoundaries.html
>http://mathworld.wolfram.com/ClassBoundaries.html
http://mathworld.wolfram.com/ClassBoundaries.html
>http://mathworld.wolfram.com/ClassBoundaries.html
http://mathworld.wolfram.com/ClassBoundaries.html
>http://mathworld.wolfram.com/ClassBoundaries.html

KILL YOURSELF
>KILL YOURSELF
KILL YOURSELF
>KILL YOURSELF
KILL YOURSELF
>KILL YOURSELF

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>>8910879
we've already been through this before in an earlier thread anon

i took 3 statistics classes in my undergrad btw

Why doesn't logarithm have a symbol like all the other common operations? Is it actually not a common operation, even though it's just the inverse of a common operation?

>>8910882
you suck

you're objectively wrong

you probably misunderstood your teacher

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>>8910886
i got a B+, an A, and an A+

>>8910891
/care

>>8910885
it does, it's log

>>8910885
It does. Its symbol is "log".

You'll hardly ever use log in another base than e. ln is fairly common.

>>8910894
It's not a symbol unless I can write it between the two inputs.

>>8910898
can you write exp between the two inputs?

>>8910898
f(x,y,z) = x^2 y log z

>>8910895
So, in practice, somebody never needs to isolate a value from an exponent unless it's finding the time at which something which grows in an e-like manner reaches a certain size?

>>8910915
log_a b = log b / log a
you dont need other bases unless it's convenient for notation

also your question is super silly and useless

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I may have gotten a C in E&M and for the major there is a majority of magnetism involved, with tha being said is this a pretty good self study book for E&M. I'm planning on doing every single problem that has a solution this summer so i'll have a better understanding of E&M as a whole.

>>8910831
>No one here's taken probability dingus

well i should have expected as much

>>8910831
>>8910929
https://www.amazon.com/David-J.-Morin/e/B00C4LDVC2/ref=dp_byline_cont_book_1

Take a look at his first book, probablity for entuhusitic beginner, I dont know if it will help you though honestly. it's 273 pages

>>8910929
be more specific. there are WILDLY different levels at which you can do probability. if it's a brainlet freshman class for engineers I don't honestly give a fuck. otherwise athreya & lahiri or k lai chung

>>8910929
we've gone through multivariable cdfs
multivariable calc is a prerec

>>8910895
log base e (aka natural logarithm) is usually written as "ln" though
"log" usually refers to base 10 or base 2 depending on whether it's in a CS context

>>8910958
that's what they tell brainlets but log almost always means e in reality

If log is used in base e so much that it's often left empty with an implied e, why isn't the same thing done for reciprocals? That is, denote a reciprocal by drawing a line above it; a fraction with no numerator. Root also uses an implied 2 when the whatever-it-is is left empty.

>>8910994
Log by itself in base 2 is only used in old-ass comp sci. Log by itself in base e is only used by Stephen Wolfram because autism. Log means base 10 unless otherwise specified, and ln is most commonly used. If you have log_n anything, it's best to change it to ln with the change of base formula.

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>tfw can't even find an equation for the sinusoidal function

The furthest I got was 1 + 2sin(z[theta - 1]) but whenever I try to solve for z, I only even get a value that satisfies only one point of the graph, not all of them.

Am I retarded?

If I have that two complex numbers, a and b, squared are equal, under what conditions are the complex number themselves equal? As in, a^2=b^2 => a=b, when?

>>8911013
since a^2 = b^2 implies 0=a^2-b^2=(a-b)(a+b) you have either a=b or a=-b

to remove the sign ambiguity you have to have b=-b, i.e. b=0 so a=0.

>>8911002
Hi retard, z=pi/2

>>8911013
Even when you take complex numbers into account, each number only has two ways to reach it via squaring. When you square a vector, you square its magnitude and double its radians.

>>8911032
But how did you find it? It has many solutions for the point I used, including pi/2, so how do you know which is the one that satisfies the whole graph?

>>8909688
I don't care about Indian accents, it's just that his is unintelligible half the time, and math videos are practically useless if you can't understand the professor

>>8908395
Bumping my question
Is there no hope?

how do i show the vector (a,b,c) is perpendicular to the plane ax+by+cz=d? i often see it stated but i dont know how to go about proving it

>>8911266
Theres a couple of ways of thinking about it. One you make the plane as a sum of two vectors with variables u and v, and the equation you have is obtained from the normal to both those vectors.
The other is to just take the grad of that plane which gets you the normal out.
Either way you then just take the dot product of the two to prove its perpendicular.

>>8907467
I have two small stupid questions

1) It is my understanding that using choice I can repeatedly pick reals from (0,1). Is the 'enumeration' I produce invalid only because you can always produce a real not in that list, or is there a better reason?

2) Wtf do we call an irreflexive, antisymmetric, transitive relation? Will 'strict partial order' do?

Thank you!

>>8911488
>Is the 'enumeration' I produce invalid only because you can always produce a real not in that list
yes
https://en.wikipedia.org/wiki/Cantor's_diagonal_argument

>>8911504
Thanks! I know this. I was just wondering (hoping) something was wrong with my using choice to pick reals

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Can someone give me a hint as to how I would do this?

>>8911881
I'll give you some hints.
For nearly all divisibilty proofs, re-express the given information in the form [math] a = q \times n + r [/math]
For digit proofs, remember that, e.g., [math] 958.3 = 9 \times 10^2 + 5 \times 10^1 + 8 \times 10^0 + 3 \times 10^{-1} [/math]

Any good way to prove that for real [math] x \geq 1 [/math],

[eqn] \ln \left( \frac{ x^{ \lfloor x \rfloor}}{ \lfloor x \rfloor ! } \right) \leq x [/eqn]

>>8912023
why do you think it's true?

>>8911881
this is like the one thing i couldn't grasp in high school. they had this shit in the first math class. they didn't even explain it they just said some rules as if they were obvious or as if you were supposed to remember them easily.

>>8912023
Try splitting the ln in 2 and use stirling's aproximation for the factorial

>>8912083
s/class/course

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>>8912073
Pic related.
Also, I am doing an exercise in analytic number theory. Prove:

[eqn] \sum_{n \leq x}^{} \frac{n}{\phi (n)} = O(x) [/eqn]

Where phi is Euler's totient function. Through a bunch of analysis I have gotten that:

[eqn] \sum_{n \leq x}^{} \frac{n}{\phi (n)} = O(\ln \left( \frac{ x^{ \lfloor x \rfloor}}{ \lfloor x \rfloor ! } \right) ) [/eqn]

So of course, if I can prove what I have in >>8912023 then I'm good to go.

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How do I prove that no number in the sequence
[eqn]1, 11, 111, 1111, \ ...[/eqn]
is a square of a number?

>>8912087
try what I >>8912084 suggested

>>8912127
>>8912084
Got it. Didn't know about that approximation.

>>8912119
A way would be to prove that there exist no squares such that their two last integers are 11.

Or if you are clever then analyze the nth term and see what you find:
[math] \frac{10^n - 1}{9} [/math]

>>8912119
1 is a perfect fucking square you moron
also 11 is the square of [math]\sqrt{11}[/math]
you're welcome, piggot

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Maybe anyone can recommend me something to read with pic related?

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>>8912401
no bully plz ):

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does anyone know what this is?
i think it's a donut shape in the fourth quadrant, but i cant check on wolframalpha

>>8910994
Group theorists sometimes do this actually.

>>8912608
hahahaha why, it's literally one key press to type the 1 above the line

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>>8912426

>>8912426
Square the inequalities and let z = x + i y with x,y real to get

(x-2)^2 + (y+2)^2 < 2
and
2 <= 4 (x-2)^2 + 4 (y+2)^2

So, yes it's a donut.

>>8912654
Well the 2 should be a 4 since it's squared too.

>>8909688
how much of a piece of shit do you have to be to not take out the garbage for your grandma

>>8912639
Most group theorists use [math]x^{-1}[/math] to mean the inverse of [math]x[/math]. The ones I'm talking use [math]\bar{x}[/math] instead (I actually prefer this notation.

I've never heard of anyone using [math]\frac{1}{x}[/math] if that's what you're talking about.

Which way do planets rotate, around themselves and the sun?
Is there a reason for the way they rotate? Do other star systems have more varied ways, if it is even possible to know?

>>8912678
>Which way do planets rotate, around themselves and the sun?

Depends how you're looking at them.

>>8912668
x^-1 is more clear, just a line above x could accidentally be misread or the line could disappear with a shitty pdf scan or something

>>8912692
Well for this question I'm asking from Earths perspective and if it is too angled then compared to Earth.

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Hey guys im an EE major physics minor and need one more upper level physics class to complete the minor Would it be jewish to take a physics class "Electromagnetic Theory" the semester after taking an EE class "Electromagnetic Field Theory"

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Why the fuck is the integral of f(t) on [a, b] equal to F(b) - F(a)?
My fucking lecturer didn't explain this shit at all.
Why anti derivatives? Why/how do they work and how are they related to this? how do derivatives even relate to this at all?
I don't get the logic at all.

Please tell me I'm not the only one who struggles with this shit.

>>8913063
When you calculate an integral at a certain value, you're calculating the area under the curve from zero up to that value. So the integral on [a,b] is the area from zero to B minus the area from zero to a.

>>8913063
First off, here f(x)=F'(x)
The formula is true intuitively because if you add up all the little, instantaneous changes in F that occur between a and b (given by f,) you end up with the total change, but really it's a special case of the fundamental theorem of calculus, just taking a constant as the upper bound of integration rather than x

>>8913063
Why would the lecturer present the FTC without proving it?

>>8913074
I understand what an integral is. It was pretty easy to find the definite integral using the lower and upper sums, and I thought it was pretty simple.
But then they introduced the FTC and now I understand nothing.

>>8913076
>First off, here f(x)=F'(x)
I know that too, but I don't know how derivatives relate to integral calculus.

>if you add up all the little, instantaneous changes in F that occur between a and b (given by f,) you end up with the total change
Is that total change equal to the area under the curve between [a, b]?

>>8913081
They did prove it, but I'm a fucking brainlet and didn't understand it.
I usually don't understand proofs.

>>8913063
Think of F(b) is the function evaluated at b which is some location on the horizontal or x-axis when evaluated it F(b) corresponds to a height therefore the statement of F(b) - F(a) is a difference in heights spatially separated by location along the number line. This difference can be conceptualized as potential

>>8913087
>They did prove it, but I'm a fucking brainlet and didn't understand it.
>I usually don't understand proofs.
Integration is the inverse function of differentiation, just like multiplication and division, and addition and subtraction. What is there to not fucking get?

>>8913081
every calculus lecturer presents the FTC without proving it...

>>8913168
which school for brainlets do you go to?

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>>8907467

Branch of physics to apply for if I was interested in electrodynamics?

>>8913148
I get that.
I just didn't understand the relation of derivates with integrals.
Now that I think about it and visualize it in my head, I guess it makes more sense now, but the way the lecturer introduced it was pretty shit and confusing I think.
I'd have to do some graphing in desmos to get a better idea.

>>8913154
The way it was explained was shit.
So the inverse derivative of a function is also called the anti-derivative of that function, which is also the integral of that function.
Did I get that right?

>>8911881
10 is congruent to 1 mod 3 and mod 9

What exactly does congruence apply to? Is pi congruent to sin(0)?

>>8913403
[math] \pi \equiv sin(0) \pmod{\pi} [/math]

>>8913408
I was asking because sin() and mod are both periodic.

>>8913476
>>8913403
congruent just means equals when you can't be assed to properly define your equivalence relation and your quotient space

Let's say we build a thinger that can lift rockets way up like 50 km high or so, and it can even give them a boost of say 200m/s. Under those conditions, what would be the specs of a rocket that needs to go at least into LEO?

The reason I ask is because I hear all the time that escaping the atmosphere is the hardest part of space travel, but what about reaching orbital velocity once you do? Isn't that hard too?

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How could I unify something like z+3 into one thing? Like with z = r*e^(ia) + 3 sdfgsdfgsdfgsdfgrstygdfdfgxdfgs

>>8913087
>muh area under the curve
The total change in F from a to b is F(b)-F(a), yes? The continuous change in F is given by F', which is f. If you add up all these little changes in F between a and b, which means integrating its rate of change F'=f from a to b, you get the total change in F, which equals what we said above.

>>8913063
https://www.youtube.com/watch?v=rjLJIVoQxz4

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So, what exactly IS Algebra?

>>8914558
the gebra

Brainlet here. Wanted to go back to school for chemistry but even the entry-level course has some crazy math requirement which I need to fulfill by passing a placement test which I've already failed twice. I haven't taken algebra/trig/calculus in 6 years and they don't give a shit about my ACT since apparently your score expires.

I have one more chance to take it but studying seems so overwhelming. All the study guides they recommend and Khan academy have hundreds of hours of videos and reading that cover all the possible material on the test. The fuck am I supposed to do

>>8912403
>>8912401
pls use 'we' instead of 'I'. It is not a diary

>>8913222
Not an expert but probably plasma physics

How much mass would have a blackhole the size of foot ball?

For real numbers x and y,
Does [math] \sqrt{x^2-y^2}=x+y ? [/math]

If [math] \sqrt{x^2-y^2}=\sqrt{x^2+(-y)^2} [/math] then [math] \sqrt{(-y)^2} [/math]would give the absolute value of y, which is always positive.
Am I missing something or is this correct?

>>8914793
Why don't you try x = 1, y = 1

\ingamemenu.ws(2113): syntax error, unexpected TOKEN_FUNCTION, expecting '{' or ';', near 'function'

function ShouldHideDLCIcons() : bool

What do?

>>8911024
did you even try

What about partial diffeqs makes it so such harder than ordinary diffeqs?

>>8914793

Both are wrong friendo. Revise properties of roots.

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Have you guys argued about this yet?
I'm pretty sure scenario A is correct.

[math](b + c)^2 - 2bc(1 + cosX) = (b + c)^2 - 4bc\,cos2\frac{1}{2}X[/math]

how the first member turns into the second member in this equation?
my trig identities are rusty as fug

>>8915423
https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Half-angle_formulae

>>8915423
[math]- 4bc\,cos2\frac{1}{2}X = - 4bc\,cos^2\frac{1}{2}X[/math]
thats the correct term, it's cosine squared not cos2

>>8915429
thx

>>8915157
obviously A.
Given that there is no resistance when the piston pushes down on the cube.

>>8915157
depends on how the game is programmed, if the object keeps its momentum relative to the portal or relative to the game world

>>8913087
Since the height of the graph determines the rate of area accumulation, the rate of change of the integral is the function.

Where can I find useful resources for newbies learning matlab and rstudio? Doing a second year engineering paper in my first year and they expect me to be able to use these programs.

Is there a term for the set of prime number subsets that the Mersenne primes belong to? That is, prime number subsets where each element is equal to an integer raised to a constant power and plus or minus a constant value.

What about a term for this, but instead of raising to powers, its using any product-based function(such as normal multiplication or the factorial function). That is, prime number subsets where each element is equal to the output of a product-based function with a constant rank, plus or minus a constant.

I'm sure this wording is fucked up. Describing things like this falls under set theory, right?

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Would some kind analyst be able to assist me with this problem?

Write down a general Taylor series approximation for the function f(x)about the point x =x subscript:n that explicitly includes terms up to fifth order derivatives and a statement denoting terms beyond fifth order using big-O notation.

I had this question in an exam, I can't find anything in my notes about Taylor's series and I can't find a process online on how to solve it, can anyone point me in the right direction to figuring this out?

Are there any theories that use Mach's principle to predict fucky physics at cosmic scales? Like, taking the idea that centrifugal forces are caused by something rotating relative to the rest of the universe, and going with the idea that bigger structures(such as galaxies) will have different centrifugal force because there is less "rest of the universe" relative to them, when compared to very small things.

>>8916313
I can find a Taylor's series given f(x) but I don't understand how to find it for a general f(x) given that point. Any tips?

>>8916393
I'm a moron, it's just a general series...

>>8912666
grandma should quit being such a lazy cunt

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how do i derive v=u+at? i get as far as pic related and im stuck. i know the LHS is v, but i dont know how im supposed to evaluate the RHS.

>>8916994

a, v and s are vector valued functions of time t, with s' = v and v' = a. Assume there is a vector valued function V satisfying V(s(t))=v(t). Then the chain rule gives

V'(s(t)) s'(t) = v'(t), so V'(s(t)) v'(t) = v'(t).

That gets you from the second integral to the third. V' is a matrix, what your pic calls
dv/ds.


s=

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do grad programs ever drug test you as part of their screening process?

>>8917556
obviously, they don't let in criminals to grad programs anymore

usually drug test + background check + penis inspection day

>>8917556
no

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Can a 25 year old NET(I'm in college) who's never worked a day in his life make it in the world?Is uni even worth it at this point? Maybe I should just sneak into uni and get contacts and friends as resources without all the bullshit.

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>>8907467
Got a bit of a medical question. Should months of daily nausea (but no vomiting or othee symptoms) be cause for concern? [spoiler]I'm only asking because the two doctors I've gone to have told me "It's just stress lmao".[/spoiler]

>>8918100
drink some fucking water

>>8918116
Nah, the globalists laced all the water with lead. I only drink alcohol now.

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>>8910614
MY SIDES

>>8918122
kys samefag

>>8918122
did you get 3 days banned and waited the whole time to reply to yourself?

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What are some good resources for learning all that I can about MRI and the brain?

How the fuck do you learn MatLab? Do you just take on a project and go from there?

>>8909688
I hope to god India and Pakistan have a nuclear war, good fucking riddance

Brainlet Anon here
Failed Algebra 2 twice before I passed it with a B
just passed Pre-Calc with a C after failing it twice.

against better judgement I am taking Calc 1 over the summer, what are some good resources or tips to ensure I don't inevitably fuck up again?

>>8910994
>it's often left empty with an implied e
Why would you do this? ln takes less characters than log.

>>8918190
Study more.

>>8918216
he means log_e. but you can also use ln

What good does it do to know that there is more than one type of infinite cardinality?

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How many of these symbols are random math notation?

>>8918291
there's an equals sign and negative sign

there's kind of a lowercase alpha but one has an arrow through it

that's it

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Please help, especially the second one.

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Any tips?

>>8918247
It is essential to the description of function spaces in functional analysis, an area which has a lot of applications in physics and the solving of partial differential equations.

Aside from that it is a very important result from set theory arguably the most important part of mathematics.

aight whiteys, can you synthetically divide by something like [math]a-4b[/math]? for example [math]\frac{a^3+64b^3}{a-4b}[/math]

>>8918633
>aight whiteys, can you synthetically divide by something like a−4b?
Yes, you can.

Suppose I have a 3D scene in which a camera is placed. The image the camera produces lies in a virtual image plane which may be oriented in any way relative to the "world corrdinate" x-y plane.
I have a 3x3 transformation matrix which lets me transform any point on the world x-y plane (2D coordinates) into 2D coordinates in the image plane. Is there an easy way to find a transformation matrix that lets me map ANY point in the world (3D coordinates) onto the image plane?

>>8918638
is it harder than long division?

>>8918655
It is long division

>>8918653
No

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>>8918653
Illustration. xc, yc, zc, focal length (not shown), intersection between pink line and XY-plane are known (that's how M is calculated). Given x0, y0, z, I want to find m, n for intersection between image plane and line through C and P1.

>>8918460
>>8918356
both trivial, what did you even try?

I was wondering if the pareto principle is a special case of Zipf's law:
Pareto's principle says that a fraction p of things is done by (1-p) of participants. Zipf's law states that when ranking things done by participants, their fraction is highestcontribution/rank

If we then put these together into one formula, we get 1+ln(px) = (1-p)(1+lnx). Now we should solve this for p and take the limit for x to infinity. But I'm somehow to stupid to do that.

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>>8918122

>>8918770
accidentially, I switched the meaning of p. But that doesn't change anything about the calculation.

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>>8918356
>>8918460
>mfw I find these super trivial as well, because of mr Langlands lite >>8918767 who nurtured me

At least try before you are given answers. Show work.

>>8918633
https://en.wikipedia.org/wiki/Polynomial_long_division

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>>8918779
>mr Langlands lite >>8918767 (You) who nurtured me

I think my pickes are too acidic and i want to measure the PH value to 1 decimal digit.

I dont want to order some chemistry kit but am willing to go to the grocery store. I have a 40% vinegar bottle and baking powder which is a mixture of NaHCO3, Na2H2P2O7 and cornstarch in unknown quantities.

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how do i make a 'liberated' CV like this one?

>>8910690
Ultra violet - svedu

>>8918923
so brave

>>8918923
https://mathematicswithoutapologies.wordpress.com/2015/12/11/piper-harron-smashes-phallogocentrism/

ahahahahahahahahahaha

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P is a set of paths p, each path p is made of edges. Edges have a weight [math]w_e[/math] and a capacity [math]c_e[/math]

I don't get the equality on the second line here, seems to me like on the left side we take all weights [math]w_e[/math], then on the right side we only took the ones that belong to the "current" path p, so why do we have an equality and not a [math]leq[/math] ?

Are there supposed to be parenthesis here ?

>>8918923
RIP mathematics

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>>8919353
>implying piper harron isnt the saviour of maths

If an electron and a positron can annihilate each other and produce two gamma ray photons, can two gamma ray photons "collide" and produce an electron and positron?

what happened to the dinosaurs? didn't noah save them?

I'm having a hard time picturing surface integrals. For example, when I calculate the surface integral over the unit sphere with f(x,y,z) = z, what does the number I get here?

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can anyone who does mechanics or something similar help me understand pic related.
should the indexes on [math]\Pi_1,\Pi_2[/math] be swapped and why is the final solution not [math] P=\sqrt{\frac{D}{g}F(\theta)} [/math]?

>>8919609
it's the surface area. try putting a rectangle or a triangle along the x axis and calculating the area. with a surface integral you're doing the same thing but the surface can have a more complicated shape.

if I hate my EE labs will I fail as an engineer?

If a series has a partial sum formula, can that always be used to tell whether or not the series diverges?

>>8919890
As long as you can evaluate the limit of it, yes

Is the area of the valley where the graph of [math]x^2-x-1[/math] dips below the x axis equal to [math]\dfrac{9+10\sqrt{5}}{2}[/math]?

>>8919931
No.

Why is /pol/ invading /sci/? Are they trying to spread propaganda?

>>8919942
They come here twice a week and on the weekends usually. Just ignore it.

>>8919942
Crossboarding != invasion, they just bait for responses because this board and /pol/ have relatively little overlap compared to other mid-speed boards. It's been happening for years, it will likely never end.

If I apply for an agricultural or horticultural job but didn't complete the degree will I immediately be bunged into the bin? A lot of places want at least a bachelor's.

>>8919942
/pol/ is the biggest board on 4chin. /pol/ memes are spreading just like /b/ memes used to spread to other boards

>>8919962
>didn't complete
If you went to school for it and didn't complete the degree, you are going to have a very hard time explaining that in way that doesn't make them >>>/trash/ your resume.

>>8919972

I wasn't a fan of school.

>>8919980
You'll have to make up a better excuse than that, something like your mom was terminally ill and you had to take care of her

[math]z=3-i3\sqrt{3}[/math]

Find [math]\arg(z)[/math]

I realise this is absurdly easy, but the solutions sheet has a different answer to what I get and I wanna make sure I'm not making some stupid mistake.

>>8919980
then they'll think you're not a fan of working

>>8919942
They're short on living space.

>>8920029
It's [math]-\frac{\pi}{3}[/math]
What does your solution sheet say?

>>8920029
http://www.wolframalpha.com/input/?i=arg(3-3sqrt(3)i)

>>8920037
Sheet gives the answer as [math]\frac{\pi}{3}[/math], I get [math]\frac{5\pi}{3}[/math], so effectively the same as your answer.

>>8920042
reminds me of when our high school math textbook had like a dozen mistakes. fucking sloppy kike shit

>>8919939
What did I do wrong?

>>8920042
No, the principal argument is between [math]-\pi[/math] and [math]\pi[/math], you're both wrong.

>>8920047
I don't know, I can't see your working out. You've either messed up finding the roots, messed up finding the integral, or messed up evaluating the integral.

>>8919994

I could theoretically do that. During my first and second years of high school we had to deal with my grandfather having Alzheimers. I could switch the dates around as long as they don't really look into it.

>>8920032

I enjoy a challenge and school wasn't very challenging.

>>8920135
>i'm too cool for school ;)
whats it like being that smart? do you find it hard to relate with non-geniuses?

>>8920139

It's boring and lonely. I do. Am to inteligant four tards.

>>8919942
>Why is /pol/ invading /sci/?
/pol/ isnt. People here just get really angry when scientific facts (such the existence of only 2 genders, IQ of blacks is statistically inferior) are voiced and start to call people Nazi and accuse them of posting on /pol/.

In fact this place is overrun with communists and other leftists scum, who only create the appearance of the right being anywhere because every time someone disagrees with them they start to wildly call people Nazis and fascists.