## Doubt regarding ordered fields

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.....
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 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus The real numbers are not an ordered field under <. Rather, the real numbers are an ordered field under $\leq$.
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