Consecutive application of Modulo Operator

Question

Is it true that $a \bmod n\equiv (a \bmod n)\bmod n$?

Is is possible to show intuitively why ?

Answer 1

$a\bmod n$ is by definition the congruence class of the remainder in the division of $a$ by $n$ .

$(a \bmod n)\bmod n$ is the congruence class of the remainder in the division of this remainder by $n$. But, as this remainder is less than $n$, the latter remainder is the first remainder itself.