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Math Help - necessity of reflexivity in equivalence relation

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    necessity of reflexivity in equivalence relation

    I somehow am messed up while reading the conditions that define equivalence relation..by symmetry property x~y implies y~x and by transitivity x~y , y~x implies x~x..so why do we need reflexivity ?
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    Re: necessity of reflexivity in equivalence relation

    Quote Originally Posted by clerk View Post
    I somehow am messed up while reading the conditions that define equivalence relation..by symmetry property x~y implies y~x and by transitivity x~y , y~x implies x~x..so why do we need reflexivity ?
    Because it is possible to have a relation on a set which is symmetric and transitive and not be reflexive.
    Some element could be missing from any pair in that relation.
    \{a,s,d\} and \{(a,a),(s,s),(a,s),(s,a)\} for example.
    Thanks from clerk
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    Re: necessity of reflexivity in equivalence relation

    thanks.
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