Definition:Square/Function

Definition

Let $\GF$ denote one of the standard number systems: $\N$, $\Z$, $\Q$, $\R$, $\C$.

Definition 1

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

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

where $\times$ denotes multiplication.

Definition 2

The square (function) on $\GF$ is the mapping $f: \GF \to \GF$ 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:

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

Examples

Example: $6$

The square of $6$ is $36$:

$6^2 = 36 = 6 \times 6$

Also see

• Equivalence of Definitions of Square Function

• Definition:Square Mapping: in the context of abstract algebra

• Definition:Square Number

• Results about the square function can be found here.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): square (as a power)