Symbols:Number Theory

$$x\backslash y$$ or $$x|y$$

These symbols mean $$x$$ is a divisor of $$y$$.

$$\backslash$$ is becoming increasingly popular since many mathematicians are of the opinion that $$|$$ is overused, and hence confusing.

The LaTeX code for $$x\backslash y$$ is "x\backslash y", and the code for $$|$$ is "|".

$$x \nmid y$$

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.

$$\lceil{x}\rceil$$

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".

$$\lfloor{x}\rfloor$$ 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". The LaTeX code for $$\left[ x\right]$$ is "\left[ x\right]".

It is advised that $$\lfloor{x}\rfloor$$ is used rather than 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".