isotonic vs monotonic?

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isotonic vs monotonic?

Postby Farabor » Fri Aug 29, 2014 9:40 pm UTC

I just encountered a professor using the term 'isotonic' in class. From my brief forays online, it seems to be either the exact same as monotonic, or something very close to it. Is there any difference in these terms?

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Re: isotonic vs monotonic?

Postby Tirian » Fri Aug 29, 2014 11:12 pm UTC

It strikes me as a more general term. For instance, if X is the set of all finite subsets of ℕ, then I'd feel more comfortable describing the traditional summation operator Σ:X->ℕ as isotonic than monotonic because the domain and codomain aren't ordered by the same relation. But I guess some people do -- it's just a matter of preference.

You might want to check to see if your professor also likes "antitone" for what you'd have called monotone decreasing functions in Calc I.

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Re: isotonic vs monotonic?

Postby Cauchy » Sat Aug 30, 2014 9:08 am UTC

I always heard it as a monotone being either isotone or antitone. "Isotone" is "the same way", "antitone" is "the opposite way", and "monotone" is "one way".
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
Thanks, skeptical scientist, for knowing symbols and giving them to me.

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