@PedroTamaroff I do that to encourage corner-cutting, to take the lazy route! You don't need to show the formal definition of convergence when you know multiplying convergent sequences converge, and so does adding them
It's to demonstrate that, "don't bother doing it the long way, you already know stuff, use it!"
@AlecTeal: Look at this answer for example, it is not overly casual but also not overly formal, and yet he uses a lot of words you wouldn't find in a normal maths textbook: math.stackexchange.com/a/37268/3787
Anyway @PedroTamaroff you should get into the habit of upvoting rather than waiting for the 5th edition of an answer, it improves confidence because it means "someone else has agreed with you"
It causes no harm, it wont "devalue" the worth of rep
But seriously I'm not going to format answers TO SIMPLE ANALYSIS questions like I am writing a textbook, nor should you expect me. The information is correct, the answer is an answer, upvotes build my confidence, I really appreciate even the comment ones it means "I have improved"
@VibhavPant no, Linus named it based on his thoughts of Perforce after they wanted to charge for use.
@AlecTeal OK. I don't mean to be comparing shoe sizes here or anything, but you just told me "you should get into the habit of upvoting rather than waiting for the 5th edition of an answer" -- I have cast almost 14.000 upvotes so far.
@AlecTeal You somehow deduced my voting habits from something I told you -- well, you didn't. But, still. It is not nice to be around prejudging people, eh? =)
@AlecTeal Wikipedia says: "Torvalds has quipped about the name git, which is British English slang meaning "unpleasant person". Torvalds said: "I'm an egotistical bastard, and I name all my projects after myself. First 'Linux', now 'git'"
@VibhavPant is that the Perforce system? Basically a company let Linux use it's usually paid for distributed VCS, then they said "pay us" everyone was like "you ****s" of course you cannot name a VCS **** so they chose "git"
@AlecTeal: If you don't want to format answers to "simple analysis questions" then you also shouldn't be complaining about people not upvoting your answers.
@PedroTamaroff you need to stop treating this site like everyone is at your level, a lot of people are not and are learning, and one nice encouraging thing from someone with high rep, or getting rep itself vastly boosts confidence and gives a sense of achievement. No one can deny this.
So stop being a [Git's working title] and use upvotes for encouragement not "Well I'm not upvoting that, I'd never publish that in a book on the subject" or whatever test it is that you use.
This applies to all of you BTW - this site is so unforgiving to new / learning people.
@AlecTeal: This site is designed to reward experts more than learning people - because it's about answering questions which often need a lot of knowledge. If you're a learning person, why do you put so much emphasis on your rep anyways?
So usually @Huy on spotting that answer I'd think "I agree with this, and they've taken the time to write it, I want to encourage this behaviour" ad upvote.
Of course, I will play by your rules and think "You know that one sentence is to long" and not bother.
@PedroTamaroff Just saying' : Why not be a little open-minded and agree that big words doesn't mean the idea should be also big? Do you think profinite groups are THAT ahead of what I am studying?
Oh and there should have been a '?' mark after etale :P
The last bit, about the connection of Galois theory with covering spaces and the dessins bit I don't know deeply, but I have heard about it from lectures some guys talked about here in the uni.
@PedroTamaroff I have no problem accepting what I don't know. I don't know the modern aspects of Gal(\bar Q/Q). Don't know about the stuff Grothendieck did. That's why I didn't write it.
@AlecTeal I usually try to help new users, for example:
Many exercises are like this: one carries into another, in increasing (or not?) difficulty. Personally, I would keep reading Spivak, and give it more time if necessary. You're always invited to drop by the chat and clear out any doubts or request help. — Pedro Tamaroff ♦yesterday
@PedroTamaroff math.stackexchange.com/a/1087558/66223 this answer here, the OP and I agree "induction" in the comments, I preform the inductive step, why would I spend more time on this when the required part he was stuck on is entirely there
@beginner what's the definition of open set? "Neighborhood to all of its points" right?
So take the plane, and take any point, you can always stick an open ball around that point, thus neighborhood to all points (I assume you know that open balls are open, the proof is easy)
At the same time it's also closed, containing all it's limit points
DUH DUH DUUUUH
See closed and open are not defined as opposites, closed means "you can't escape it" like addition on the integers is closed, you cannot leave the integers @beginner
@beginner now "open" doesn't mean you can escape it, it means "neighborhood to all of it's points" so if I give you a point you can go alittle above and a little below, which is important for defining differentiability.
@Studentmath A space X is simply connected if every loop based at points of X is contractible. If you don't know homotopy, it's a bit hard to formally define it.
@Studentmath If you have a two paths $\sigma_1, \sigma_2 : [0, 1] \to X$ in a topological space X with same basepoints, i.e., $\sigma_1(0) = \sigma_2(0) = x_0$ and $\sigma_1(1) = \sigma_2(1) = x_1$ then these two paths are said to be homotopic if there is a map $H : [0, 1]^2 \to X$ such that $H(0, t) = x_0$, $H(1, t) = x_1$ and $H(s, 0) = \sigma_1$ and $H(s, 1) = \sigma_2$.
i.e., you have a square and you're squeezing the two sides of the square so that the two sides go to a point
and the upper edge and the lower edge map to the two paths
