why bash increment: `n=0;((n++));` return error? n=0; ((n++));echo "ret=$?;n=$n;" ((n++));echo "ret=$?;n=$n;" ((n++));echo "ret=$?;n=$n;" from `n=1` on, `((n++))` works correctly, only when `n=0`, `((n++))` return error, and I am using a `trap '' ERR` that is causing trouble with that is it some bug?

It's because the return value of `(( expression ))` is not used for error indication. From the `bash` manpage:

> (( _expression_ ))
>
> The _expression_ is evaluated according to the rules described below under **ARITHMETIC EVALUATION**. If the value of the expression is non-zero, the return status is 0; otherwise the return status is 1. This is exactly equivalent to **let** " _expression_ ".

So, in your case, because the value of the expression **is** zero, the return status of `(( ... ))` is 1.