@WouterZeldenthuis Well the orientation (given that it's orientable) is given locally, so you should only have to check in a suitable chart; this shouldn't be hard.
@shobon "an adjunction in a groupoid 1234567"? that was flagged as not an answer, and it is not an answer without more explanation. There was an unanswered request for more detail. If you have more detail and you wish to edit it, I will undelete it.
@shobon Please make the answers here as self-contained as possible. We don't like link only or "see Wikipedia" answers. Links can go bad and why would people look here if all they wanted was what was on Wikipedia? They come here for more information, examples, etc.
One doubt: Is this site suitable for discussing puzzles, (puzzles of mathematical inclination)?. For example : The hat problem.100 prisoners are lined up and asked what the color of hat behind?.
HELP!! Could please someone with a background in group theory read my answer in math.stackexchange.com/questions/319812 and in particular the comments. If I get him right, MartinBrandenburg is saying that that my argument is void. I just don't get it.
Shobon, I sincerely apologize for offending you with my comment. I meant it sincerely. I thought your argument was clever and straightforward, although it happened not to work for this particular problem.
So when I came in and saw you, I thought I would compliment you. I did not think you would take it as a personal insult, since I was not speaking of you personally, but only of something that you wrote.
My question is: Is there a common term to describe a property of a group element which, whenever it holds for some element $g$ must also hold for all conjugates of $g$? For example, the property of being central is of this type.
Incidentally, since Shobon has since deleted his answer, I am going to say here what it is. The question was to show that there exists a perfect square whose digits sum to 2011. Shobon replied "There's not. Since 2+0+1+1=3 the number would be divisible by 3, but it's a square so it would be divisible by 9, but then its digit sum would be too."
extremity: for uniform convergence, you need to find a single epsilon that works for every point. For pointwise convergence, each point can have a different epsilon.
@boywholived If you are serious that my apology could reasonably be interpreted as an insult, I would be grateful for an explanation. I thought you were joking.
@MJD say i have a sequence of function given by f_n(x)=arctan(nx). and say that x is in [0,\infty), can you tell me (if you have the time) why its not uniformly continuous?
So if someone gives you a delta, and you think you have an epsilon to show that arctan nx is continuous for all n, then someone can take a very large n so that arctan is extremely steep near 0, so steep that your epsilon is not small enough to bound arctan nx within delta.
Changes in the school curriculum over the last few decades have resulted in many students finding Analysis very difficult. The author believes that Analysis nowadays has an unjustified reputation for being hard, caused by the traditional university approach of providing students with a highly polished exposition in lectures and associated textbooks that make it impossible for the average learner to grasp the core ideas.
