Put a relation on $C[0,1]$ by $f\sim g$ if $f(k/10)=g(k/10)$ for $k$ with $0\le k \le10$
I have shown that this is an equivalence relation, but I have no idea what are the equivalence classes. It requires me to prove together with addition of eq class and scalar multiplication, it makes $C[0,1]/\sim$ into a vector space of dimension 11.
So I guess I have something to do with $k/10$. Any hints?