An example of an operation in ordinary arithmetic that is idempotent I came across this question in the book Axiomatic set theory by Suppes:

Can you give an example of an operation of ordinary arithmetic which is idempotent?

So, here I have some things that I cannot completly understand and I need your help: 


*

*What is the meaning of ordinary arithmetic? I would understand that it means $+$ and $\times$ on $\mathbb R$, but I'm not sure.

*Does the meaning of an operation which is idempotent mean for all the elements of the universe? I mean I can think of $1$ in $\times$ or $0$ in $+$ because $1\times 1=1$ and $0+0=0$, does this count? 

Here is a binary idempotent operation: $a*b=(a+b)/2$.
