Symbols:Number Theory

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Symbols used in Number Theory

Divides, Divisor, Factor

$x \divides y$

This means:

$x$ is a divisor (or factor) of $y$

or:

$x$ divides $y$.


The $\LaTeX$ code for \(x \divides y\) is x \divides y .


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 .


Ceiling

$\ceiling x$

The ceiling function of $x$: the smallest integer greater than or equal to $x$.


The $\LaTeX$ code for \(\ceiling x\) is \ceiling x .


Floor

$\floor x$

The floor function of $x$: for $x \in \R$, the greatest integer less than or equal to $x$.


The $\LaTeX$ code for \(\floor x\) is \floor x .


Coprime

$x \perp y$

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


That is:

$\gcd \set {x, y} = 1$

where $\gcd$ denotes the greatest common divisor of $x$ and $y$.


The $\LaTeX$ code for \(\perp\) is \perp .


Deprecated Symbols

This page contains symbols which may or may not be in current use, but are either non-standard in mathematics or have been superseded by their more modern variants.

On $\mathsf{Pr} \infty \mathsf{fWiki}$ the intention is to present a consistent style, and so these symbols are to be considered deprecated.


Divisor

$x \mid y$

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


The symbol $\mid$ has been (or is in the process of being) superseded by $\divides$, which is becoming increasingly popular since many mathematicians are of the opinion that $\mid$ is overused, and hence a possible cause for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


The $\LaTeX$ code for \(\mid\) is \mid .


Integer Part

$\sqbrk x$


For $x \in \R$, the greatest integer less than or equal to $x$.

That is, it is the integer part of a given real number.


$\sqbrk x$ has been (or is in the process of being) superseded by $\floor x$, due to the already widespread uses of square brackets.


The $\LaTeX$ code for \(\sqbrk x\) is \sqbrk x .