/sqt/ - Stupid Questions Thread: Saturday Night Edition

>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?

>FSU
Former Soviet Union?

>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

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

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?

shit, i don't think i know either

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:

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

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

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.

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

elementary row operations are just multiplying by elementary matrices tho

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.

>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?

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

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

>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

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

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

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

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

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

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

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

r/The_Donald

lots of great stuff, it's way better htan Veeky Forums. you should go there and never post here again

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

i think i'll stay here

>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?

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

>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

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

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

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

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

now fuck offfff

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

imageboard policing doesn't look good on you

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

>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

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

I get it man, fucking indian accent.

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?

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

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.

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

are calculus labs mostly optional?

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.

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.

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

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

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

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

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

roll two dice

the probability of the dice adding up to 1 is 0

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

That it can't happen

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?

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

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?

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

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

There's theory behind it.

How would you assign probability to these events

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.

see

>but the probability itself is non-zero

Why?

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

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

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

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.

*does that mean

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...

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

what does class width have to do with anything here?

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

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

Go away.

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

>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)?

shitty bait. just look at

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.

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

2(1-0.999...)

...

KILL YOURSELF

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

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

...

not an arguement

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

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

Ok. I'll Alta Vista this term.

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

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

kys this is as fucking stupid as the width bullshit

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.

en.wikipedia.org/wiki/Ad_hominem

stay clueless freshman, i bet you don't even have a degree

...