My sister just asked this question to me: “Is an irrational number odd or even?” I told her that decimals are not odd or even and that does imply that not recurring and non repeating decimals will also not be odd or even. But I want a rigorous math proof for this. Can someone help me with this proof? Also, can I do this proof by contradiction?

**Answer**

Definition.

Let $n\in \mathbb{Z}$ be an integer. $n$ is called even if …

According to the definition only integers are even or odd. It is not something that you have to prove.

**Attribution***Source : Link , Question Author : Community , Answer Author : Thomas*