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The normal ceiling and floor functions, denoted $\lceil x \rceil$ and $\lfloor x \rfloor$ respectively, refer to the smallest integer greater than or equal to $x$, and similar for the floor function.

I have a need for some notation to represent the smallest integer strictly greater than $x$, or similar for 'strict floor'.

I've had a google and nothing came up, and I'd prefer not to make up notation if some already exists. Has anyone come across notation for this before?

Cameron Martin
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3 Answers3

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It seems that strict ceil is equal to $ 1 - \lceil - x \rceil $, and srtict floor is $ - 1 - \lfloor - x \rfloor $.

Hope that helps.

lisyarus
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In addition to the answers given, I would like to add:

If you cannot easily find the notation for what you are doing, it is definitely not standardized (the Schur/Hadamard product comes to mind). You can also expect the reader not to be familiar with any notation, and thus choose what's most convenient.

Just be sure to define the notation clearly in whatever report/thesis/assignemnt you are writing.

naslundx
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  • @JordanGlen Oops, I meant it to be cursive. That looks better. – naslundx Apr 13 '15 at 13:14
  • I'd definitely define it for the reader regardless of which notation I used, I was more looking for examples that other people had come up with, so I can pick one that I like. From the answers I'm getting, maybe I didn't make that clear enough. – Cameron Martin Apr 13 '15 at 13:16
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How about use $\lceil x+\rceil$ for the strict ceiling, and $\lfloor x-\rfloor$ for strict floor? (Sometimes we write $f(x+):= \lim_{u\downarrow x} f(u)$ and $f(x-):= \lim_{u\uparrow x}f(u)$.)

Zhenyao Sun
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