Command Substitution Shell Expansions Process Substitution
Arithmetic expansion allows the evaluation of an arithmetic expression and the substitution of the result. The format for arithmetic expansion is:
$(( expression ))
The expression is treated as if it were within double quotes, but a double quote inside the parentheses is not treated specially. All tokens in the expression undergo parameter expansion, command substitution, and quote removal. Arithmetic substitutions may be nested.
The evaluation is performed according to the rules listed below (see Shell Arithmetic). If the expression is invalid, Bash prints a message indicating failure to the standard error and no substitution occurs.
Command Substitution Shell Expansions Process Substitution