[EM] What is the most useful definition of "monotonicity"?

Kristofer Munsterhjelm km_elmet at t-online.de
Tue Nov 24 15:45:05 PST 2020

On 16/11/2020 03.32, Rob Lanphier wrote:

> That's nine different criteria that all could be called
> "monotonicity".  This raises a few questions for me:
> 1. Is Woodall's definition correct?
> 2. Is Woodall's definition the most useful?
> 3. Is Woodall's definition overly-complicated, or just
> appropriately-complicated?
> 4. Does breaking up monotonicity into nine different criteria make it
> easier to understand, or harder?
> 5. Was Woodall just copying his definition from someone else when
> publishing those nine criteria?  If so, who?

"Monotonicity" is almost always mono-raise. So maybe the Monotonicity
article could detail mono-raise and then have a disambiguation
section or something like it for the other types of monotonicity; kind
of like how the clone independence page is mainly about Tideman's
concept, although Woodall split the clone independence criterion into
three of his own (clone-no-help, clone-no-harm, clone-in).

I'm not myself aware of any paper that uses unqualified "monotonicity"
to mean something else than mono-raise. Authors that refer to e.g.
mono-add-top tend to say mono-add-top.

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