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0 pointsthaumasiotes10y ago0 comments

Not so.

http://mathworld.wolfram.com/MonotoneIncreasing.html

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3 comments · 1 top-level

ddlatham10y ago· 2 in thread

So.

http://mathworld.wolfram.com/MonotonicFunction.html

https://en.wikipedia.org/wiki/Monotonic_function

thaumasiotesOP10y ago

You think the definition of "monotonic function" is more relevant to the meaning of "monotonically increasing sequence" than the definition of "monotone increasing" is?

[1,1,2], [1,1,1], and [1,2,2] are not monotone increasing. They're also not monotonic functions.

Sadgrinner10y ago

In all seriousness, the definition of monotonically increasing that I was taught is the same as exists in wikipedia:

"A function is called monotonically increasing (also increasing or non-decreasing), if for all x and y such that x <= y one has f(x) <= f(y).

https://en.wikipedia.org/wiki/Monotonic_function#/media/File...

This definition allows for 'flatness' in a graph, since the derivative does not change sign.

Or, from http://www-history.mcs.st-and.ac.uk/~john/analysis/Lectures/... :

    A sequence f(n) is monotonic increasing if f(n+1) ≥ f(n) for all n ∈ N.
    The sequence is *strictly* monotonic increasing if we have > in the definition instead of ≥.

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