Doubt regarding ordered fields

ashok vardhan

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.....

micromass

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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ashok vardhan	Doubt regarding ordered fields Tweet 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.....

micromass 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 [itex]\leq[/itex].