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== Metaphor in denoting sets ==
Since so much of mathematics consists in discovering and exploiting patterns, it is perhaps not surprising that there should have arisen various set-denotational conventions that strike practitioners as obvious or natural—if sometimes only once the pattern has been pointed out.
This is total bullshit
One class comprises those notations deriving the symbol for a set from the algebraic form of a representative element of the set. As an example, consider the set of even numbers. Since a number {{math|''b''}} is even precisely if there exists some integer {{math|''a''}} such that {{math|''b'' {{=}} 2''a''}}, the following [[Set-builder_notation#Terms_more_complicated_than_a_single_variable|variation on set-builder notation]] could be used to denote this set: {{math|{2''a'' : ''a''∈'''Z'''}}} (compare this with the formal set-builder notation: {{math|{''b''∈'''Z''' : ∃ ''a''∈'''Z''': ''b'' {{=}} 2''a''}}}). Alternatively, a single symbol for the set of even numbers is {{math|2'''Z'''}}. Likewise, since any odd number must have the form {{math|2''a'' + 1}} for some integer {{math|''a''}}, the set of odd numbers may be denoted {{math|2'''Z'''+1}}.
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