Difference between revisions of "Cartesian product"
(New page: The '''Cartesian product''' of two sets <math>A</math> and <math>B</math> is the set of all ordered pairs <math>(a,b)</math> such that <math>a</math> is an element of <math>A</...) |
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The '''Cartesian product''' of two [[set]]s <math>A</math> and <math>B</math> is the set of all [[ordered pair]]s <math>(a,b)</math> such that <math>a</math> is an [[element]] of <math>A</math> and <math>b</math> is an [[element]] of <math>B</math>. More generally, the Cartesian product of an ordered family of sets <math>A_1, A_2, \dotsc</math> is the set <math>A_1 \times A_2 \times \dotsb</math> of [[ordered tuples]] <math>(a_1, a_2, \dotsb)</math> such that <math>a_j</math> is an element of <math>A_j</math>, for any positive integer <math>j</math> for which we have specified a set <math>A_j</math>. | The '''Cartesian product''' of two [[set]]s <math>A</math> and <math>B</math> is the set of all [[ordered pair]]s <math>(a,b)</math> such that <math>a</math> is an [[element]] of <math>A</math> and <math>b</math> is an [[element]] of <math>B</math>. More generally, the Cartesian product of an ordered family of sets <math>A_1, A_2, \dotsc</math> is the set <math>A_1 \times A_2 \times \dotsb</math> of [[ordered tuples]] <math>(a_1, a_2, \dotsb)</math> such that <math>a_j</math> is an element of <math>A_j</math>, for any positive integer <math>j</math> for which we have specified a set <math>A_j</math>. | ||
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| + | == Proof of Existence == | ||
== See Also == | == See Also == | ||
Revision as of 18:02, 29 August 2024
The Cartesian product of two sets 
and 
is the set of all ordered pairs 
such that 
is an element of and 
is an element of . More generally, the Cartesian product of an ordered family of sets 
is the set 
of ordered tuples 
such that 
is an element of 
, for any positive integer 
for which we have specified a set .
Proof of Existence
See Also
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