# Thread: Find a function (ideals)

1. ## Find a function (ideals)

Hl! I do not understand this exercise

Recall that $\mathbb{R}^\mathbb{R}$ , the set of all real valued funtions of a real variable, is a commutative ring under pointwise addition and multiplication.
Let $n\geq{0}$ be an integer, and let $I_n$ be the set of all functions in $\mathbb{R}^\mathbb{R}$ vanishing on integer multiples of $n$

Find a function that is in $I_8$ but not in $I_4$

I do not understand why $I_n$ is an ideal and I can not find the function

Thanks

2. ## Re: Find a function (ideals)

$f(x) = \sin \left( \dfrac{\pi}{8} x \right)$

$f(8n)=0, f(8n+4)=(-1)^n$

Ok thanks