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## Homework Statement

Is the following a vector space:

The set of all periodic functions of period 1? ( i.e. f(x+1)=f(x) )

## Homework Equations

If v1 and v2 are in V then v1 + v2 is in V

If v1 is in V then c*v1 is in V where c is a scalar

## The Attempt at a Solution

I'm thinking no because a function like:

f(x) = 2*x mod 2

If you multiply by 1/2 you have

f(x) = x mod 2

What I'm wondering is if the mod 2 is effected by the scalar multiplication of 1/2. Is it or is this not a subspace? Thanks for your time.