Symbols:Number Theory

Divides, Divisor, Factor

 * $x\backslash y$

This means "$x$ is a divisor (or factor) of $y$", or "$x$ divides $y$".

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

The $\LaTeX$ code for $x\backslash y$ is x \backslash y.

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 $y$.

The $\LaTeX$ code for $x \nmid y$ is x \nmid y.

This symbol is preferable to $x \not \backslash y$ (x \not \backslash y) and $x \not | y$ (x \not | y) due to the somewhat confusing appearance of these symbols.

Ceiling

 * $\lceil{x}\rceil$

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

The $\LaTeX$ code for $\lceil{x}\rceil$ is \lceil {x} \rceil.

Note that, as with other surrounding symbols such as parenthesis and brackets, if the height of the interior function is not a standard size, as with $\left \lceil {\frac{\frac x y}{\frac a b}} \right \rceil$, it is necessary to write the function as \left \lceil {x} \right \rceil.

Floor
$\lfloor{x}\rfloor$ or $\left[x \right]$

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

The $\LaTeX$ code for $\lfloor{x}\rfloor$ is \lfloor {x} \rfloor.

$\lfloor{x}\rfloor$ is gaining in popularity over the more traditional $\left[x \right]$, due to the already varied uses of square brackets.

Note that, as with other surrounding symbols such as parenthesis and brackets, if the height of the interior function is not a standard size, as with $\left \lfloor {\frac{\frac{x}{y}}{\frac{a}{b}}} \right \rfloor$, it is necessary to write the function as \left \lfloor {x} \right \rfloor.

= Deprecated Symbols =

Divisor
$x|y$

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

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

The $\LaTeX$ code for $|$ is |</tt> or \vert</tt>.

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

Floor, or Integral Part
$\left[ x\right]$

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

The $\LaTeX$ code for $\left[ x\right]$ is \left[ {x} \right]</tt>.

$\left[ x\right]$ has been (or is in the process of being) supeseded by $\lfloor{x}\rfloor$, due to the already varied uses of square brackets.