Re:What is the Axiom of Choice?
by threatofrain on Friday July 16, 2021 @10:30AM
(#27856578)
What's the consequence of extending the reals with infinities, as my textbook for real analysis does?
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That every closed set has a maximum and a minimum.
Relatedly, every set gets a supremum and an infumum. (The first two must be members of the set. The second two can lie outside the set).
Without the extension, you need to make an exception for unbounded sets with the above rules.