# Ceiling and floor operators used for min max

1. Dec 8, 2015

### quantum__2000

I remember seeing somewhere people using symbols for ceiling and floor operators together with super/subscripts as substitutes for min and max. Example:
$$\lceil x \rceil ^k$$
to mean min(x,k).

Has anyone ever seen this? Where? Thanks!

2. Dec 8, 2015

### micromass

Staff Emeritus
I'm sorry, I haven't seen this. But I just wanted to say that this certainly ranks among the top 10 worst notations I've ever seen.

3. Dec 8, 2015

### Staff: Mentor

I haven't seen the notation as you used it, to give the minimum of two numbers, but I have seen this:
$\lceil x \rceil$, also called the smallest integer function. It is defined as being the smallest integer that is greater than or equal to x. Many programming languages, including C, C++, and others, have a ceiling function, ceil(x), that does this.
For example, $\lceil 1.8 \rceil = 2$.

The counterpart is the floor function, or greatest integer function, denoted $\lfloor x \rfloor$. C, C++, and others have floor(x). This is defined as the largest integer that is less than or equal to x.
For example, $\lfloor 2.35 \rfloor = 2$.

I agree with micromass that $\lceil x \rceil^k$ is terrible notation.

4. Dec 8, 2015

### jbriggs444

It would be a reasonable notation for denoting the smallest multiple of k greater than or equal to x. That is, the generalization of ceiling to a modulus other than 1.

5. Dec 9, 2015

### mathexam

Yes, that's definitely incorrect notation and most people will confuse it as exponents. As someone else stated, the notation that is correct and seen in programming languages is [7.8]=8 or [5.1]=5. These are more standard and less likely to be confused.