So i understand that to be an ordering, you have to satisfy the conditions of being reflexive, anti-symmetric, and transitive and for linear-ordering , there should be any a,b such that a ≤ b or b ≤ a but I can't seem to find the connection unless maybe defining some elements to exist in the ordered set.
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4What is your definition for a well-order if it is not a priori a linear order? – Henno Brandsma Mar 20 '18 at 15:52
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@HennoBrandsma An order relation for which for every non-empty subset there is a minimum. Not mention of linear ordering, although it gets implied since minimum must in particular be comparable to the other elements of the subset. So, it does require a proof. – SphericalTriangle Mar 20 '18 at 15:57
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Then my answer does work. – Henno Brandsma Mar 20 '18 at 16:04
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Aren't reflexive and anti-symmetric contradictory? – Acccumulation Mar 20 '18 at 16:41
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@Acccumulation antisymmetric is $x \le y, y \le x \to x=y$. not $x < x$ is called asymmetric, I believe. – Henno Brandsma Mar 20 '18 at 17:35
