Are limits rigourous? They seem to just be "oh, just eyeball where that function seems to be going"
Are you still in Calc 1?
>>7946273
>he has never done an epsilon delta proof
RUDIN
>>7946273
Yes, the limit is well defined. The limit is defined as follows:
if
[math]
\forall \epsilon > 0 \exists \delta \text( s. t. ) x \in x_0 \pm \delta \implies | f(x) - L | < \epsilon
[/math]
which means the limit as x approaches x0 = L
Is the definition of shitposting rigorous?
saged and hidden/
>what are epsilon-delta proofs
>>7946284
>>7946288
Mfw sages get overridden
>>7946310
kawaii ether
any functions that appear to converge then just flip out and do something else?
I have no shame
>>7946320
something like
[math]f(x)=\sum_{n=100}^x\frac{1}{n*log(n)*log(log(n))}[/math] diverges unbelievably slowly.
>>7946328
[eqn]f(x) = \sum_{n=100}^{x \frac{1}{ n * log(n) * log( log(n) )} }[/eqn] You're welcome.
>>7946326
looks like one of those final fantasy things
>>7946336
ok i laughed
>>7946334
>>7946346
[eqn]f(x) = \sum_{n=100}^x \frac{1}{ n * log(n) * log( log(n) )}[/eqn]
>>7946354
Thank you magic anon
>>7946368
I a-actually enjoy it!!
>>7946368
>implying limits can be defined at all
>implying you can make uncountably infinitely many statements
>implying you can even define [math]\mathbb{R}[/math], let along topological spaces
Fucking kek. Enjoy your shaky fundamentals.
>he uses metric crap
>/a/utists think this is their pedophilia spamming board
>>7946481
you don't know how to use the
>R
meme at all. you don't need anything remotely weird (including countable infinity) to have topological spaces.
>>7946368
You need it for the basic limits
>>7946273
As they're done in first year calc, absolutely not. In a first complex analysis class, you can't even evaluate infinite limits directly. You prove f(z), z to infinity is equal to f(1/z) z, z to zero and use that instead.
>>7947122
>not using the extended complex plane
>>7947247
>impling proving anything about it doesn't involve looking at the function in charts, ie. doing exactly what he says
>>7946336
Asians?
>>7946281
what does s.t. means
>>7946281
that is still just eye-balling where the function seems going, epsilon can just get smaller, and smaller, how is that not eyeballing where the function is going
>>7947367
Suck titties
>>7946281
if for all epsidol larger than 0 exists delta of s.t. x in x0 plus or minus delta implies that absolute value of f(x) - Limit is smaller than epsilon.
Makes no sense, you call that rigorous? Go to jail.
>>7947391
That was the shittiest thing I ever read. Do you even know what your words mean?
>>7947404
I just translated that guys' definition of limits into human speech.
That is what those symbols mean, except for maybe the thing with delta and s.t.
>>7947424
Ah alright. I'm on mobile so latex isn't displaying and I didn't bother translating his post.
A good definition is as follows
We say the limit of a function f as f approaches x0 is L if for all positive M there exists a positive N such that for all x in (x0-N,x0+N), we have that |f(x)-L)<N.
>>7947424
Also, "s.t." stands for "such that"
You might also see "WLOG" which is "without loss of generality"
>>7947367
self-titled
>>7946481
Wildhamburger
>>7947441
Why don't we have a fancy korean alphabet symbol for 'such that' like we do for 'in all' and 'exists'?
Can we sue the oxford dictionary?
>>7946481
>>7947442
That's s/t
>>7946273
I don't understand what you're trying to ask.
Don't you know the definition of a limit? Just check the wikipedia
>>7947444
You use a vertical bar | for "such that".
>>7947122
You are talking about something completely different. If I understand you correctly, you're referring to taking the residue at infinity, which is Res(f, inf)= -Res((1/(z^2))f(1/z), 0). How you connected this with limits of a function is beyond me.
>>7947367
It means "such that" anon. Ignore these trolls, this board should be for learning, not incessant shitposting
>>7947806
>/sci/ is for serious discussion
>>7947826
Leave
>>7946481
>can't define topological spaces
you mean a set X along with a collection T of subsets of S such that the three axioms of a topology are satisfied
Huh I guess I can't
>>7947438
>yfw the first guy literally wrote that
>>7946273
Yes. You can take the analytical approach:
Show that for each epsilon > 0 there exists a delta > 0 such that for all x within distance delta of x_0, f(x) is within distance epsilon of y, then the limit of f(x) where x approaches x_0 is equal to y. In other words: if to be close to the proposed limit just requires you to be close to the argument, then the limit is as proposed.
Then you have the topological approach, where you talk about opens around a point, and a sequence which converges to that point if there is, for every open containing the point, always some term after which every term in the sequence is in the open.
There are more ways of doing these things when you get out of the reals. There is a whole field of complex analysis concerned with stuff like that on spaces like C.
>>7947854
basically, yes, you eye-ball where it converges.
>>7946281
How do you solve for L from there?
>>7948324
(You)
>>7948324
[math]\lim_{x \rightarrow c} f(x) = L[/math]
>>7948324
u dont
>>7947828
With all honesty, no u
>>7946368
>he hasn't taken analysis
Kek
>>7948324
You just eyeball where the function is going
>>7950481
actually, you just eyeball where the function converges
>>7950457
way to look silly, post went over your head. taking introductory analysis doesn't make you an expert, so you might want to consider there are reasons people say the things they say
read the other replies and you might get a hint to what it means, newfriend
>>7947828
>>7947826 here
>>7950176 is correct, you should leave.
>>7946281
hurr durr, the difference between the actual limit and a value very close ([math]f(x)[/math]) to it its very small.
this doesnt prove shit
>>7950952
hey math teacher
when am i gonna use limits in life?
like its just a bunch of numbers
wtf
Read Analysis 1 by Tao
>>7950955
limits are useful in derivatives, for finding slope of functions and areas of functions, you can use that knowledge for most of physics. Do calculations, economics, literally everything.
>>7950979
Did my bait taste good?
>>7946368
>NUH UHHHH!
>YOU GUYS DON'T UNDERSTAND! I'M MUCH SMARTER THAN YOU
Just fuck off with your le smug anime face
>>7951001
Not that guy but...
>le
tfw redditors really do come on here
>>7950984
fuck off to reddit
>>7951567
>>>pole
bamp
>>7952980
wow you saved a beatiful thread from dying
