Cartesian Product
Chapter 7: Front Matter · Knowledge Base · EN medium
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We know that the Cartesian product of sets is nothing but a set of ordered elements. In particular, Cartesian product of two sets is a set of ordered pairs, while the Cartesian product of three sets is a set of ordered triplets. Precisely, let A, B and C be three sets. Then the Cartesian product of A with B is denoted by A × B . It is defined by A × B = { ( a, b ) : a ∈ A, b ∈ B } . Similarly, the Cartesian product A × B × C is defined by A × B × C = { ( a, b, c ) : a ∈ A, b ∈ B, c ∈ C } . Thus A × A = { ( a, b ) : a, b ∈ A } . Is it correct to say A × A = { ( a, a ) : a ∈ A } ?
📖 Namma Kalvi 11th Maths Textbook Volume 1 English Medium · Page 12
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We know that the Cartesian product of sets is nothing but a set of ordered elements. In particular, Cartesian product of two sets is a set of ordered pairs, while the Cartesian product of three sets is a set of ordered triplets. Precisely, let A, B and C be three sets. Then the Cartesian product of A with B is denoted by A × B .
It is defined by A × B = { ( a, b ) : a ∈ A, b ∈ B } . Similarly, the Cartesian product A × B × C is defined by A × B × C = { ( a, b, c ) : a ∈ A, b ∈ B, c ∈ C } . Thus A × A = { ( a, b ) : a, b ∈ A } . Is it correct to say A × A = { ( a, a ) : a ∈ A } ?
It is important that the elements of the Cartesian product are ordered and hence, for non-empty sets, A × B = B × A, unless A = B. That is, for non-empty sets A × B = B × A if and only if A = B. We know that R denotes the set of real numbers and
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