How to call a monotonic function that takes a value?

Question

I'm looking for a name for a family of functions that are characterized by:

$f: \mathbb{N} \rightarrow \mathbb{N}$
$f$ monotonic
$\exists x \in \mathbb{N} \;.\; f(x) = 0$

(Assuming $0 \in \mathbb{N}.$)

@Clayton that looks like a comprehensive answer to me. – Anthony Carapetis Sep 06 '13 at 14:33 — Anthony Carapetis, Sep 06 '13 at 14:33
Right @Clayton, do you want to post this as answer? – thpani Sep 06 '13 at 14:47 — thpani, Sep 06 '13 at 14:47
@AnthonyCarapetis: Posted as an answer. Thanks. – Clayton Sep 06 '13 at 18:07 — Clayton, Sep 06 '13 at 18:07
@thpani: Posted as an answer. Thanks. – Clayton Sep 06 '13 at 18:11 — Clayton, Sep 06 '13 at 18:11

Clayton · Accepted Answer · 2013-09-06T18:13:19.177

0

Since you're assuming $0\in\Bbb N$, if $f$ is increasing, most people would just say $f(0)=0$ or if it is decreasing, $f$ is eventually zero.

Edit: Before the question edit, it wasn't explicitly stated that $0\in\Bbb N$. In this case, if you AREN'T assuming $0\in \Bbb N$, it's called the empty set.

edited Sep 06 '13 at 18:13

answered Sep 06 '13 at 18:06

Clayton

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How to call a monotonic function that takes a value?

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