The POSIX specification for the test and [ commands includes a few arithmetic tests for integers:

• [ "$a" -eq "$b" ]: Equal
• [ "$a" -ne "$b" ]: Not equal
• [ "$a" -lt "$b" ]: Less than
• [ "$a" -le "$b" ]: Less than or equal to
• [ "$a" -gt "$b" ]: Greater than
• [ "$a" -ge "$b" ]: Greater than or equal to

Sometimes using these tests with expansion of arithmetic expressions can be unwieldy to write; for example, if we wanted to test whether the value of the bytes variable, divided by 1,000, was greater than the kbytes variable, we might write:

if [ "$((bytes / 1000))" -gt "$kbytes" ] ; then
    ...
fi

Bash includes its own syntax for testing arithmetic expressions with (( – without a leading $ sign – including all the terms in one expression, which is somewhat easier to read and debug:

if ((bytes / 1000 > kbytes)) ; then
    ...
fi

The double parentheses, ((...)), can contain any arithmetic expression, like we saw in Chapter 5, Variables and Patterns, and it is treated like a command – its exit value reflects the outcome of the expression. An outcome of 0 is treated as false and exits with status 1, and any other outcome is treated as true, and exits with status 0:

((2 > 0))  # True; exits 0
((a = 1))  # True; exits 0, and variable a is assigned the value 1
((0 > 3))  # False; exits 1
((0))      # False; exits 1
((a = 0))  # False; exits 1, and variable a is assigned value 0

These expressions are very powerful and somewhat easier to manipulate than their POSIX-standardized equivalents. Remember that all of the arithmetic operations use integers only – no fractional (fixed or floating point) numbers.