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If nothing else is specified, does the term "monotonically increasing integers" mean that $$f(k+1)+1 = f(k), \forall k \in \mathbb{N}$$ or

$$f(k+1) \geq f(k), \forall k \in \mathbb{N}$$

Rebellos
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Alex5207
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    It means a sequence of integers that is increasing. – Jakobian Mar 07 '19 at 18:51
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    The second is true I believe. If it is by an integer amount each time it should be of the form: $$f(k+1)=f(k)+c$$ – Henry Lee Mar 07 '19 at 18:51
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    The phrase "monotonically increasing integers" in isolation is pretty much meaningless. What is the full context in which it appears? – Eric Wofsey Mar 07 '19 at 19:15
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    Assuming you mean "a monotonically increasing sequence of integers," it's a little ambiguous between $f(k+1) \ge f(k)$ ("nondecreasing") and $f(k+1) > f(k)$ ("strictly increasing"). – Qiaochu Yuan Mar 07 '19 at 20:23

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