Ceiling and floor operators used for min max

In summary, there is a notation for the ceiling function, denoted as ##\lceil x \rceil##, which gives the smallest integer greater than or equal to x. There is also a counterpart, the floor function, denoted as ##\lfloor x \rfloor##, which gives the largest integer less than or equal to x. While some people have seen the use of super/subscripts with ceiling and floor operators as substitutes for min and max, this is not a widely accepted notation. The more common notation is [x], where x is the number being operated on, to denote the ceiling or floor function.
  • #1
quantum__2000
1
0
I remember seeing somewhere people using symbols for ceiling and floor operators together with super/subscripts as substitutes for min and max. Example:
[tex]\lceil x \rceil ^k[/tex]
to mean min(x,k).

Has anyone ever seen this? Where? Thanks!
 
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  • #2
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
quantum__2000 said:
I remember seeing somewhere people using symbols for ceiling and floor operators together with super/subscripts as substitutes for min and max. Example:
[tex]\lceil x \rceil ^k[/tex]
to mean min(x,k).

Has anyone ever seen this? Where? Thanks!
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
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.
 
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Likes ElijahRockers
  • #5
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.
 

What is the purpose of ceiling and floor operators used for min max?

The ceiling and floor operators are mathematical tools used to determine the upper and lower bounds of a set of data. These operators are often used in optimization problems, where finding the maximum and minimum values is essential for finding the optimal solution.

How do ceiling and floor operators work?

The ceiling operator, denoted by the symbol ⌈x⌉, rounds a number up to the nearest integer. On the other hand, the floor operator, denoted by the symbol ⌊x⌋, rounds a number down to the nearest integer. Both operators essentially "snap" a number to the nearest whole number, either up or down.

Can ceiling and floor operators be used for non-numeric data?

No, ceiling and floor operators are specifically designed for numerical data. They cannot be applied to non-numeric data, such as strings or characters.

What are some real-world applications of ceiling and floor operators?

Ceiling and floor operators are commonly used in various fields, such as finance, economics, and computer science. For example, in finance, these operators can be used to determine the maximum and minimum values of stock prices, while in computer science, they can be used to optimize algorithms and calculations.

Are there any limitations to using ceiling and floor operators?

One limitation of ceiling and floor operators is that they only work with discrete values. This means that they cannot be used for continuous data, such as decimals or fractions. Additionally, these operators may not always provide the most accurate or optimal solution, as they simply round a number to the nearest integer without considering other factors.

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