#202204281446 could be expressed in Set-Builder Notation like \(\{a \in S | P(x)\}\) which means the set of all elements \(a\) in \(S\) such that \(P(X)\) is true. (\(\{\) and \(\}\) denote the set of all, \(|\) denote such that) This could be written as \(\{a | P(x)\}\).
Set-Builder Notation
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Set
Set is a collection of elements where their order and recurrence does not matter. It could be specified using either 202204281704# or 202204281700#. Due to the properties of set, the set \(\{a, b, c\}\) is same with \(\{b, a, c\}\) and \(\{a, a, b, c, c, c\}\), which could be denoted as \(\{a, b, c\} \equiv \{b, a, c\} \equiv \{a, a, b, c, c, c\}\).
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Function
Based on this definition, the unique element in \(B\) related to \(x\) by \(F\) is denoted \(F(x)\), read “F of x”. We can understand it as \(F(x)\) is the output or result of input \(x\) in the function \(F\). A function could be express in 202204281700 as \(F = \{(x, y) \in A \times B|y = F(x)\}\). (relation is a 202204281535 of 202204281601 of \(A\) and \(B\))
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Cartesian Product
A Cartesian Product of two #202204281446 \(A\) and \(B\), is the set of all #202204281552 \((a, b)\) where \(a \in A\) and \(b \in B\). It is denoted as \(A \times B\) which read as “A cross B”. This could be expressed in 202204281700# as \(A \times B = \{(a, b) \in S|a \in A \ \text{and}\ b \in B\}\).