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For a recursive equation I am working on, I need the ability to describe rounding up/down to the nearest value within an ordered set. For instance, let S = $\{ 5x \mid x \in Z \}$. Now suppose I want to represent rounding up from $7.3$ to the nearest $y \in S = 10$, and a way to represent rounding down from $3.9$ to the nearest $z \in S = 0$. Is there any kind of standard notation or the like that I can use for this?

I am using the floor and ceil function syntax would probably be confusing in this context - though presently that is how I'm writing it out for lack of anything better. Please advise! Thanks :)

Asaf Karagila
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Ryan Pierce Williams
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    I don't think there is a standard notation for this. I would use $$\min S_{\ge x}$$ For example $$10= \min_{\ge 7.3} 5 \Bbb Z$$ If your set is of the form $m \Bbb Z$, then you can use the floor function $$5= 5 \lfloor \frac{7.3}{5} \rfloor$$ – Crostul Jan 13 '23 at 09:32
  • @Crostul I like that - thanks :) – Ryan Pierce Williams Jan 13 '23 at 09:34

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