# Simple Group on Integers Concept

PLease keep this to an intro abstract algebra level.

My book sayas that the set of all nonnegative integers (including 0) under addition is not a group because there is an identity element 0, but no inverse for 2

I don't understand what that part means.

Is it saying $2 + 0 \neq 0 + 2$?

Also for the natural numbers, why is there no identity element?

$0$ is an identity element because $n+0=0+n=n$ holds for all $n\in\mathbb N_0$. On the other hand, if $2$ had an inverse $x$, then we would have $2+x=x+2=0$. But there is (provably) no $x\in \mathbb N_0$ with this property.