Na página bash
man:
((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".
E mais:
Arithmetic Expansion Arithmetic expansion allows the evaluation of an arithmetic expression and the substitution of the result. The format for arithmetic expansion is: $((expression))
Qualquer coisa colocada em parênteses duplos torna-se uma expressão matemática que bash
avaliará.