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  3. assume that for any subset s of , if xs and y/s, t

Assume that for any subset S of , if XS and Y/S, then XY intersects...

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Accounting

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Assume that for any subset S of , if XS and Y/S, then XY intersects the boundary of S. (This assumption is nontrivial, and requires the Least Upper Bound axiom for R ). Using this assumption, prove that if S is any closed, bounded set in the plane and which has a circle C as its boundary, then S is actually the closed disk with the same center and radius as C, or is CC itself. Assume that for any subset S of , if XS and Y/S, then XY intersects the boundary of S. (This assumption is nontrivial, and requires the Least Upper Bound axiom for R ). Using this assumption, prove that if S is any closed, bounded set in the plane and which has a circle C as its boundary, then S is actually the closed disk with the same center and radius as C, or is CC itself

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