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monotonically nondecreasing (Definition)

A sequence $(s_n)$ (with real elements) is called monotonically nondecreasing if

$$ s_m \ge s_n \;\forall\; m > n $$

Similarly, a real function $f(x)$ is called monotonically nondecreasing if

$$ f(x) \ge f(y) \;\forall\; x > y $$

Compare this to monotonically increasing.

Conflict note. In other contexts, such as [1], this is called monotonically increasing (despite the fact that the sequence could be ``flat.'' In such a context, our definition of ``monotonically increasing'' is called strictly increasing.

Bibliography

1
``monotonically increasing,'' from the NIST Dictionary of Algorithms and Data Structures, Paul E. Black, ed.




"monotonically nondecreasing" is owned by akrowne.
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See Also: monotonically nonincreasing

Other names:  monotone nondecreasing

Attachments:
limit of nondecreasing sequence (Theorem) by pahio
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Cross-references: monotonically increasing, real function, real, sequence
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This is version 5 of monotonically nondecreasing, born on 2002-02-18, modified 2005-08-16.
Object id is 2136, canonical name is MonotonicallyNondecreasing.
Accessed 7978 times total.

Classification:
AMS MSC40-00 (Sequences, series, summability :: General reference works )

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