Variations

Arithmetic expansion with backticks (often used in conjunction with expr)

z=`expr $z + 3`          # The 'expr' command performs the expansion.

Arithmetic expansion with double parentheses, and using let

The use of backticks (backquotes) in arithmetic expansion has been superseded by double parentheses -- ((...)) and $((...)) -- and also by the very convenient let construction.

z=$(($z+3))
z=$((z+3))                                  #  Also correct.
                                            #  Within double parentheses,
                                            #+ parameter dereferencing
                                            #+ is optional.

# $((EXPRESSION)) is arithmetic expansion.  #  Not to be confused with
                                            #+ command substitution.



# You may also use operations within double parentheses without assignment.

  n=0
  echo "n = $n"                             # n = 0

  (( n += 1 ))                              # Increment.
# (( $n += 1 )) is incorrect!
  echo "n = $n"                             # n = 1


let z=z+3
let "z += 3"  #  Quotes permit the use of spaces in variable assignment.
              #  The 'let' operator actually performs arithmetic evaluation,
              #+ rather than expansion.

Examples of arithmetic expansion in scripts:

1. Example 16.9, “Using expr”

2. Example 11.15, “Simple while loop”

3. Example 27.1, “Simple array usage”

4. Example 27.11, “The Bubble Sort”

5. Example A.16, “tree: Displaying a directory tree”