Recent content by Tchakra

I am looking at hatcher's book and one excercise asks to determine if there exist a short exact sequence: 0 \rightarrow \mathbb{Z}_{4}\rightarrow \mathbb{Z}_{8} \oplus\mathbb{Z}_{2} \rightarrow \mathbb{Z}_{4} \rightarrow 0 Now when i look at that i have absolutely no idea where to start...

Hey, can anyone help me with this please. I am doing algebraic topology and am particularly stuck on exact sequences. I "understand" the idea of the definition for example: 0\rightarrow A\stackrel{\alpha}{\rightarrow}B\stackrel{\beta}{\rightarrow}C\rightarrow 0 in this short exact...

I had a perfectly valid reason at the time :-p, f(x)= x/|x| , if you discount to consider the point x=0 which i didn't.

I just realized my mistake, my third point is wrong. The Euler characteristic is different ...

I am having difficulties grasping the consequences of this theorem, would really appreciate a little enlightenment. A: Well, the statement of the theorem is clear, that Every closed Surface is homeomorphic to: 1) a sphere, 2) the connected sum of g tori 3) or the connected sum of g...

I will admit defeat as much as i hate it :cry: :mad: , ok i was wrong. I meant a*tan btw, but doesn't matter anyway.

Gablar, I never believe in any scientific idea unless it is maths(but that isn't science), and yet i am the first to spout about it when explaining stuff. physics is a model and as the name suggest a model if but a way to understand reality and not reality itself. So if a better model comes...

I can't get to construct two good functions now, but take, f(x)= -1/x - 2 and construct g(x)= atan(bx) + c where a, b and c such that g(-1/2)=0 and blows up at g(0). Strictly in (-1/2,0), f(-1/2) = g(-1/2) and as x -> 0 f,g -> infinity I don't know if in this case f>g, but as x -> 0 either f...

I didnt know that anyone looked for practicality in mathematics at the level of asking about infinity, or that it conforms to intiuition.

i think you missed my constraint "asymptotic at a", which self implies that a is not \infty

I think you meant "the spatial (y,z)". Either way whichever you meant. the 2d space at no point contained a sphere, it only contained a circle, and moving it along one axis doesn't not change the containance of any 2dimendional plane. According to our knowledge, Time is a pure geometrical...

CRgreathouse is right. on both counts. the number of elements(called cardinality) in (0,1) is equal to the cardinality of (0,2) which is equal to the number of numbers in the real. The problem many people have with ithe concept of infinity in mathematics is that they try to think of it as a...