| Cartesian Product |
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| CATEGORIES ABOUT CARTESIAN PRODUCT | |
| basic concepts in set theory | |
| binary operations | |
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Specifically, the Cartesian product of two Set s ''X'' (for example the points on an x-axis) and ''Y'' (for example the points on a y-axis), denoted ''X'' × ''Y'', is the set of all possible Ordered Pair s whose first component is a member of ''X'' and whose second component is a member of ''Y'' (e.g. the whole of the x-y plane): | ||
| :''X''<sup>''n''</sup> | ''X'' × ''X'' × × ''X'' = <math> \{(x_1, \ldots, x_n) x_1\in X\\mathrm{and}\\ldots\\mathrm{and}\x_n\in X\}</math> |
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| :<math>\prod {i \in I} X I | \{ f : I o \bigcup_{i \in I} X_i\ \ ( orall i)(f(i) \in X_i)\},</math> |
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