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>.

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.