How do I know $a+a+...+a$ $n$ times is $na$ For a cardinal $a$ and a positive integer $n$
This seems almost trivial but I’m not sure how I can show it is true. Is it defined to be this way or must it be shown?

It is a consequence of distrbutive law that is since
$$n=\overbrace{1+1+\ldots+1}^{\text{n times}}$$
then
$$a \cdot n=a\cdot (1+1+\ldots+1)=\overbrace{a+a+\ldots+a}^{\text{n times}}$$
