((expression))
The expression is evaluated according to the rules described
below under ARITHMETIC EVALUATION. If the value of the expres‐
sion is non-zero, the return status is 0; otherwise the return
status is 1. This is exactly equivalent to let "expression".
[[ expression ]]
Return a status of 0 or 1 depending on the evaluation of the
conditional expression expression. Expressions are composed of
the primaries described below under CONDITIONAL EXPRESSIONS.
Word splitting and pathname expansion are not performed on the
words between the [[ and ]]; tilde expansion, parameter and
variable expansion, arithmetic expansion, command substitution,
process substitution, and quote removal are performed. Condi‐
tional operators such as -f must be unquoted to be recognized as
primaries.
Isso cobre o básico sobre os tipos de expressões bash e é da página man bash. Para mais expressões aritméticas, consulte este link.
Fontes:
man bash