For a set X with a relation of partial order R the element x in X is called the least element of X if, for all y in X, x relates to y (xRy). Prove that in a partially ordered set there exists at most one least element.
If each of \(\displaystyle a~\&~b\) is a least element in \(\displaystyle X\) then \(\displaystyle a \prec b~\&~b \prec a\).
Why is that true? What does that a about \(\displaystyle a~\&~b\)?
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