LetRbe a partial order relation on a setA.

Prove that ifx belonging toAis a maximum then it is maximal.

Prove that ifxbelonging toAis a minimum and a maximum thenA={x}.

someone can help me???

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- Dec 28th 2008, 04:15 AMtukilalaPartial Order - maximum minimum and maximalLet
*R*be a partial order relation on a set*A*.

Prove that if*x belonging to**A*is a maximum then it is maximal.

Prove that if*x**belonging to**A*is a minimum and a maximum then*A=*{*x*}.

someone can help me??? - Dec 28th 2008, 08:43 AMHallsofIvy
Those look like they should be easy if you know the definitions.

What is the difference betweeen a "partially ordered set" and a "linearly ordered set"? What is the difference between "maximal" and "maximum". And, most importantly, what do "maximum" and "minimum" mean?