According to wikipedia a total order ≤ on a set X is one such that(adsbygoogle = window.adsbygoogle || []).push({});

If a ≤ b and b ≤ a then a = b (antisymmetry);

If a ≤ b and b ≤ c then a ≤ c (transitivity);

a ≤ b or b ≤ a (totality).

I'm wondering why antisymmetry is a condition since, as far as I can see, totality discounts antisymmetry. So suppose I'm trying to prove that R is a total order would it be sufficient to prove only transitivity and totality?

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# Basic confusion about a linear order.

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