Re: Long Continuous proof

$\displaystyle Consider\ SO(2)\subset\ M_{2}(R),\ A\in SO(2) if\ detA = 1. Prove\ that\ SO(2)

is\ a\ closed\ subset\ in\ M_{2}(R)$

there's another part to the question. analysis really is the hardest module. the uni blackboard is really quite a mess of 100s pages just for this module, i just need any help to get me in the right direction thanks :)

Re: Long Continuous proof

Why are you wrapping every thing is [tex] [/tex] ?

**Only put your equations in tex tags, not plain text.**

Re: Long Continuous proof

for me i think it'll be quicker eventually. why does it not read well? any advice for the question though?

Re: Long Continuous proof

Quote:

Originally Posted by

**maxgunn555** why does it not read well? any advice for the question though?

Well, I for one will bother to read through it.

I started to edit it but gave up.

I doubt many will be willing to deal with it.

Re: Long Continuous proof

yeah you're right, you can't have letters written like they're maths letters its look weird and is quicker not to.

Re: Long Continuous proof

Re: Long Continuous proof

the point is, det is a function from $\displaystyle \mathbb{R}^4\to \mathbb{R}$. you should already know that s(x,y) = x+y is continuous from $\displaystyle \mathbb{R}^2\to \mathbb{R}$, and that p(x,y) = xy is continuous from $\displaystyle \mathbb{R}^2\to \mathbb{R}$.

so det(a,b,c,d) = s(p(a,d),-p(b,c)), which is a composition of continuous maps, yes?