Symbols:Number Theory

Divides, Divisor, Factor

 * $x \divides y$

This means:
 * $x$ is a divisor (or factor) of $y$

or:
 * $x$ divides $y$.

$\divides$ is gaining in popularity over $\mid$, since many mathematicians are of the opinion that $\mid$ is overused, and hence confusing.

See Set Operations and Relations: Set Difference for an alternative definitions of this symbol.

Does Not Divide, Is Not a Divisor or Factor

 * $x \nmid y$

This means $x$ is not a divisor of $y$.

This symbol is preferable to $x \not \backslash y$ due to the somewhat confusing appearance of this symbol.

Ceiling

 * $\ceiling x$

This represents the smallest integer greater than or equal to $x$. (See Definition:Ceiling Function).

Floor

 * $\floor x$ or $\sqbrk x$

This represents the greatest integer less than or equal to $x$. (See Definition:Floor Function).

$\floor x$ is gaining in popularity over the more traditional $\sqbrk x$, due to the already varied uses of square brackets.

Coprime

 * $x \perp y$

This denotes the statement that $x$ is coprime to $y$.

That is, that $\gcd \left\{{x, y}\right\} = 1$, where $\gcd$ denotes the greatest common divisor.

Divisor

 * $x \mid y$

This means $x$ is a divisor of $y$.

$\mid$ has been (or is in the process of being) superseded by $\divides$, which is becoming increasingly popular since many mathematicians are of the opinion that $|$ is overused, and hence a possible cause for confusion.

In the context of computer languages, $\mid$ is frequently called pipe from its use in. This name is catching on in general mathematics.

Floor, or Integral Part

 * $\sqbrk x$

This represents the greatest integer less than or equal to $x$. (See Definition:Floor Function).

$\sqbrk x$ has been (or is in the process of being) superseded by $\floor x$, due to the already widespread uses of square brackets.