Definition:Square/Function

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Definition

Let $\F$ denote one of the standard classes of numbers: $\N$, $\Z$, $\Q$, $\R$, $\C$.


Definition 1

The square (function) on $\F$ is the mapping $f: \F \to \F$ defined as:

$\forall x \in \F: \map f x = x \times x$

where $\times$ denotes multiplication.


Definition 2

The square (function) on $\F$ is the mapping $f: \F \to \F$ defined as:

$\forall x \in \F: \map f x = x^2$

where $x^2$ denotes the $2$nd power of $x$.


Square Function in Specific Number Systems

Specific contexts in which the square function is used include the following:

Real Square Function

The (real) square function is the real function $f: \R \to \R$ defined as:

$\forall x \in \R: \map f x = x^2$


Integer Square Function

The (integer) square function is the integer function $f: \Z \to \Z$ defined as:

$\forall x \in \Z: \map f x = x^2$


Also see

  • Results about the square function can be found here.