About the Rules & Moderation category (Part 1)

[Zugzwang]

@May

nyaaaaaaaaaaa ok now I have no idea how to do these

[May]

I was just posting because it involves the formal definition of a limit

[Atlas]

now you know how i feel anytime y’all post mathematics

[benguinedparbecue]

the set of x in X such that the sequence of the functions evaluated at x has a limit in R = (f_j - f_k) inverse of (-1/n, 1/n) where you take the intersection of all n from 1 to infinity and the union of all j from 1 to infinity but only the intersection where j = k

[benguinedparbecue]

i think?

[benguinedparbecue]

note that i don’t know enough theory to know why this would be true

[benguinedparbecue]

in general you can prove equality by proving each side is a subset of the other but idk if you need to do that here

[May]

Explanation attempt for myself, to ensure I can do it after class:

The definition of a series with a limit: take 1/n for any n, basically an arbitrarily small number: there’s two elements of the series who are separated by no more than that arbitrarily small number. Basically, they get infinitely close.

If a limit exists, the absolute value of the difference between some f_j and f_k should be smaller than 1/n, meaning f_j - f_k is contained within the open interval (-1/n, 1/n). So that right bit is just saying, like, all the area where for ANY n, there’s some f_j and f_k whose difference is smaller than 1/n. Which is the definition of a limit.

The second one… I have to prove that the stuff on the right is an S-measurable subset, which I haven’t quite done.

[benguinedparbecue]

@May

The definition of a series with a limit: take 1/n for any n, basically an arbitrarily small number: there’s two elements of the series who are separated by no more than that arbitrarily small number. Basically, they get infinitely close.

did they really teach you epsilon convergence without mentioning epsilon

[May]

I wasn’t taught any of that

[May]

They just expected me to know it. So I figured it out

[Atlas]

they prolly told you during 3rd grade and you forgot

[May]

Also the explanation was deliberately very informal

[benguinedparbecue]

for ANY epsilon greater than 0 successive points should get within epsilon of each other and never stop being within epsilon of each other

[benguinedparbecue]

also a series is actually a sequence of partial sums

[benguinedparbecue]

(tbf for ANY epsilon greater than 0 there’s a natural number n such that 1/n < epsilon. so whatever. but where’s the epsilon spirit)

[Zugzwang]

@May

Explanation attempt for myself, to ensure I can do it after class:

The definition of a series with a limit: take 1/n for any n, basically an arbitrarily small number: there’s two elements of the series who are separated by no more than that arbitrarily small number. Basically, they get infinitely close.

If a limit exists, the absolute value of the difference between some f_j and f_k should be smaller than 1/n, meaning f_j - f_k is contained within the open interval (-1/n, 1/n). So that right bit is just saying, like, all the area where for ANY n, there’s some f_j and f_k whose difference is smaller than 1/n. Which is the definition of a limit.

NYAAAAAAAAAAAAAAAAAAA ok I get it now

[Zugzwang]

do you think tutuu is potatocat thbthbthtbhtbthbth

[Zugzwang]

like I think this is a pretty strange reason not to join

if anyone was really enthusiastic about playing, they’d probably have joined by now

[Atlas]

i advise nobody to answer that question until spectator chat is opened