Question

Prove that any function is direct sum of odd and even functions

Answer 1

id prove that U∩WU∩W={00}. But proving that any function from R to R can be displayed as a sum of odds and evens wasn't a success. I tried saying that for v∈V,w∈W:v=v−w+wv∈V,w∈W:v=v−w+w and proving that v−w∈Uv−w∈U but that didn't work (That trick worked with some linear transformations we saw, but this isn't a linear transformation).

Answer 2

I hope this helps you