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(2) Let X be a set and < a linear order on X. Let S be...

(2) Let X be a set and < a linear order on X. Let S be a subset of X. Show that if S has a least element, then S has a unique least element.

(3) Give an example, where S has no least element. (Be sure to specify what X, < and S are!)

(4) Let X be a set and < a linear order on X. Let S be a subset of X which is bounded below. Show that if S has a greatest lower bound, then S has a unique greatest lower bound.

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