What does ! mean in math

[crisp lily]

factorial

n! = 1 * 2 * 3 * 4...* (n-1) * n

so 5! = 1 * 2 * 3 * 4 * 5 = 120

[little fractal]

it means factorial

which means that if it comes after a number it multiplies it by all the natural numbers before it

[fallen ingot]

Can also mean not

Like x != y means x is not equal to y

[crisp lily]

isn't that usually ¬?

[fallen ingot]

Unfortunately there are multiple symbols for like every logic symbol

But yeah it is usually that thing

¬

[ashen pawn]

It can also mean “unique”

Like when people use symbols for statements , e.g. the backwards E for “there exists” they could go

E!x: Ax=y

For “there exists a unique x such that Ax=y”

[open temple]

Lol there's lot of meaning for !

For computer science !x = not x which is the Boolean algebraic opposite of x

For regular maths x! Is factorial of x, !x is the subfactorial of x

Also in certain programming language they also use the notation != For not equal to, ex: python

[ionic totem]

He said only maths so factorial is the most appropriate answer

[open temple]

yeah but u mút also include subfactorial ngl

*must

[fleet path]

yes

[boreal yew]

To summarize what's been said:
! can be used for factorial and subfactorials.
! can be used for negation or inequality. For mathematics, it's primarily useful for writing mathematics on a text document.
! can also represent uniqueness. As noted, ∃! can mean "there exists a unique...". Also in category theory, ! can be used to represent the unique arrow into a terminal object or from an initial object. Useful in composing arrows.