If I have a partial order, is the following conclusion valid? $a \geq c$ $b \geq c$
Then, $a = b $
Does the result change if the partial order were to become a total order? Any and all explanations would be helpful. Cheers.
Follow-up: This seems quite obvious but I'm curious nonetheless. First, call S a finite subset of the naturals. Now define a and b with the same definition:
$a, b \geq n$ for all n in S. Does it follow that a = b by definition? From a method standpoint, is it enough to draw an equality between two elements by showing that those elements are defined in the same way?