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'cube of a number'
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| Title of object: |
cube of a number |
| Canonical Name: |
CubeOfANumber |
| Type: |
Definition |
| Created on: |
2005-03-08 19:08:41 |
| Modified on: |
2005-03-08 19:20:35 |
| Classification: |
msc:20-00 |
| Synonyms: |
cube of a number=cube
cube of a number=third power |
Preamble:
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Content:
The {\em 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 (cg. general associativity).
The ``cube function'' \,$x\mapsto x^3$\, from $\mathbb{R}$ to $\mathbb{R}$ injective, but from $\mathbb{C}$ to $\mathbb{C}$ not; one has \,$x^3 = y^3$\, always when \,$\frac{x}{y} = \frac{-1\pm i\sqrt{3}}{2}$. |
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