Quiz 1 Key
1. (a) Infimum is 0, supremum is 3.
√
(b) Infimum is 0, supremum is 7.
2. (a) Infimum is 0, supremum is 1.
(b) Infimum is 0, supremum does not exist!
3. Since A is bounded above there is some M such that x ≤ M for all
x ∈ A. Then for any x ∈ A we have
cx ≤ cM
(multiplication of both sides of the inequality by a POSITIVE c preserves the inequality) so that cM is an upper bound for the elements
of B. Thus B is bounded above.
NOTE, there is absolutely no need to invoke suprema or such! It was
not given that F has the least upper bound property.
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