The distance of a number from zero on the number line, always expressed as a non-negative value. The absolute value of both 5 and -5 is 5, written as |5| = |-5| = 5.
From Latin 'absolutus' meaning free from restriction or complete, combined with 'value.' The concept developed as mathematicians worked with negative numbers and needed a way to express magnitude without regard to direction. The notation |x| was introduced in the 19th century.
Absolute value captures the essence of 'how far' without caring about direction - it's the mathematical equivalent of asking 'how much' rather than 'which way'! This concept becomes incredibly powerful in advanced mathematics, generalizing to define distance in abstract spaces and enabling everything from calculus to computer graphics.
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