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Example Questions
Example Question #5 : The Real Number System
Determine whether the following statement is true or false:
If is a nonempty subset of
, then
has a finite infimum and it is an element of
.
Possible Answers:
True
False
Correct answer:
True
Explanation:
According to the Well-Ordered Principal this statement is true. The following proof illuminate its truth.
Suppose is nonempty. From there, it is known that
is bounded above, by
.
Therefore, by the Completeness Axiom the supremum of exists.
Furthermore, if has a supremum, then
, thus in this particular case
.
Thus by the Reflection Principal,
exists and
.
Therefore proving the statement in question true.
Teresa
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