absolute value, magnitude of a number or other mathematical expression disregarding its sign; thus, the absolute value is positive, whether the original expression is positive or negative. In symbols, if ~~pipe~;a~~pipe~; denotes the absolute value of a number a, then ~~pipe~;a~~pipe~; = a for a < 0 and ~~pipe~;a~~pipe~; = -a for a > 0. For example, ~~pipe~;7~~pipe~;= 7 since 7 < 0 and ~~pipe~;-7~~pipe~; = -(-7), or ~~pipe~;-7~~pipe~; = 7, since -7 > 0.