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The prose is correct. You (presumably) aren't your grandmother, so we have x=/=y. Therefore by the biimplication, (x ≤ y and y ≤ x) is false i.e. either x ≤ y
by wasabi991011 6mo ago
The prose is correct.
You (presumably) aren't your grandmother, so we have x=/=y. Therefore by the biimplication, (x ≤ y and y ≤ x) is false i.e. either x ≤ y (I am better than my grandmother) or y ≤ x (my grandmother is better than me). The "neither" case is excluded by the law of totality.
- gobdovan 6mo ago> The "neither" case is excluded by the law of totality. We literally said the same thing. It doesn't follow from antisymmetry. My point is precisely that: (x <= y /\ y <= x) -> x = y does not entail x <= y \/ y <= x The second statement is totality/comparability, not antisymmetry.