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In the current version of my book (related with order theory) I used the term monotone to denote $\forall x,y:(x\geq y\Rightarrow f(x)\geq f(y))$.

  1. Should this usage of the term monotone be considered correct, or should the term increasing be used instead?

  2. If I switch to the term increasing, how to reformulate such phrase as "Monotonicity is obvious." or "by monotonicity of composition"?

porton
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    non-decreasing would be more accurate. – bsbb4 May 07 '18 at 13:29
  • I think the mathematical community has been kind of stuck for quite a while with ambiguous terminology for this concept. Look at this question for example: https://math.stackexchange.com/questions/115912/why-do-we-use-non-increasing-instead-of-decreasing?rq=1 – Lee Mosher May 07 '18 at 13:29
  • Increasing is stronger than monotonous. "Monotonous growth is obvious." –  May 07 '18 at 13:30
  • It would be an excellent service if you could present a reasonable and consistent terminology in your book. – Lee Mosher May 07 '18 at 13:30
  • @LukasKofler I think, non-decreasing would instead mean $\forall x,y:(x\ngeq y\Rightarrow f(x)\ngeq f(y))$. Or do I mistake? – porton May 07 '18 at 13:31
  • @LukasKofler Or does non-decreasing mean $\forall x,y:(x\geq y\Rightarrow f(x)\nleq f(y))$? – porton May 07 '18 at 13:33
  • Note it is order theory, not calculus – porton May 07 '18 at 13:35

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