Unformatted text preview: a is not an upper bound of B (as c is the least such) so some b ∈ B satisﬁes a < b ; however, this disqualiﬁes b from being a lower bound of A . Thus c ( ∈ B ) is indeed a lower bound of A . (ii) If b ( ∈ B ) is a lower bound of A then b 6 c (as c is an upper bound of B ) so that c is indeed greatest among the lower bounds of A . Notice that: (i) in proving c to be a lower bound of A we used the fact that c is the least upper bound of B ; (ii) in proving that c is the greatest lower bound of A we used the fact that c is an upper bound of B . 1...
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This note was uploaded on 11/12/2011 for the course MAS 3300 taught by Professor Staff during the Fall '08 term at University of Florida.
- Fall '08