S Property, B be a

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter7: Real And Complex Numbers
Section7.1: The Field Of Real Numbers
Problem 2TFE: Label each of the following statements as either true or false. Every upper bound of a nonempty set ...
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2. Let S be an ordered set with the greatest lower
property, B be
a nonempty
subset of S, and
bound
B be bounded above. Let L be the set of all upper
bounds of B. The x =
in S and x = 's
α = Sup
B.
= infL exists
Transcribed Image Text:2. Let S be an ordered set with the greatest lower property, B be a nonempty subset of S, and bound B be bounded above. Let L be the set of all upper bounds of B. The x = in S and x = 's α = Sup B. = infL exists
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Um.... in the problem statement, there is no mention of B being bounded below and L isn't the set of lower bounds of B.

The given info is:

  • S is an ordered set with G.L.B proerty
  • B is a nonempty subset of S
  • B is bounded above
  • L is the set of all upper bounds of B

Want to prove:

  • a = inf L exists in S
  • a = sup B

Could someone give a more detailed response?

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