Supremum is the least upper bound

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Homework Statement



Prove that the supremum is the least upper bound

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The Attempt at a Solution



Proof: let x be an upper bound of a set S then x>=supS (by definition). If there exists an upper bound y and y<=SupS then y is not an upper bound (contradiction) therefore every upper bound is greater than SupS so SupS is the least upper bound.

Is that proof correct?

Thank you.
 

Answers and Replies

  • #2
HallsofIvy
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Please tell what your definitions of "supremum" and "least upper bound" are! As far as I know "supremum" is just another name for "least upper bound" and there is nothing to prove.
 

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