In mathematics, functions between ordered sets are monotonic (or monotone) if they preserve the given order. These functions first arose in calculus and were later generalized to the more abstract setting of order theory. Although the concepts generally agree, the two disciplines have developed a slightly different terminology. While in calculus, one often talks about functions being monotonically increasing and monotonically decreasing, order theory prefers the terms monotone and antitone or order-preserving and order-reversing, respectively.

 

from: http://www.answers.com/topic/monotonic-function?hl=monotonically

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