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# cube of a number

The cube of a number $x$ is the third power $x^{3}$ of $x$. Similarly one may speak of the cube of an element $x$ in any semigroup with the operation denoted multiplicatively (cf. general associativity).

The volume of a cube (i.e. regular hexahedron) with edge length $a$ is $a^{3}$; hence the name.

The cube function $x\mapsto x^{3}$ from $\mathbb{R}$ to $\mathbb{R}$ is injective, but not as a mapping from $\mathbb{C}$ to $\mathbb{C}$; one has $x^{3}=y^{3}$ always when $\frac{x}{y}=\frac{-1\pm i\sqrt{3}}{2}$, the primitive third root of unity.

Defines:

cube function

Related:

SquareOfANumber, PowerFunction, CubeRoot, CubanPrime, SemicubicalParabola

Synonym:

cube, third power

Type of Math Object:

Definition

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

20-00*no label found*

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