# Well defined operations

1. Oct 16, 2011

### The1TL

1. The problem statement, all variables and given/known data

Let C(R) be th set of all continuous functions on ℝ and let O be the germs
of continuous functions at the origin. We have a natural surjective map π : C(R) → O. Define addition and multiplication in O by, [f ] ⊕ [g] = [f + g], [f ] ⊗ [g] = [f g].

Prove that the above operations are well defined

((This means, you must prove that if f ∼ F and g ∼ G, then f + g ∼ F + G and fg ∼ FG.))

2. Relevant equations

3. The attempt at a solution

I have no idea where to even start with this problem. My teacher tends to include problems on homework that do not pertain to his teachings or anything in our text. I have searched the internet to try to find more about how to solve this sort of problem but I cannot find anything. Any help is greatly appreciated.

Last edited: Oct 16, 2011