Question 975490
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A set cannot have a supremum that is infinity.  A supremum is a number, whereas infinity is not.  If S = {1}, and S is a subset of T, then T must contain the element 1, and then 1 is the smallest element of T that is greater than or equal to all elements of S.  Supremum and Least Upper Bound being equivalent terms, 1 is also the Least Upper Bound.  Similarly, 1 is the infimum or greatest lower bound.


Note that if set S was defined as all real numbers in the open interval *[tex \Large 0\ <\ x\ < 1] and T is the set of all real numbers, neither the supremum of S nor the infimum of S are actually elements of S.  Here the supremum is 1 and the infimum is 0.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \