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Doubt regarding ordered fields

  1. Jul 25, 2012 #1
    Sir,i have read in wikipedia that for a relation to be ordered it should be transitive,antisymmetric,total...however we know that Real numbers is an ordered field under relation "<" but antisymmetric property is not valid with "<" relation..how is this justified..rectify me.....
  2. jcsd
  3. Jul 25, 2012 #2


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    The real numbers are not an ordered field under <.
    Rather, the real numbers are an ordered field under [itex]\leq[/itex].
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