True-False Practice for Exam 3

These are just for practice and don't affect your grade. I'm assuming you have read Ch 1.1 - 2.4 of Wade's book. Assume the universal set is U = R.


True False. If E has a supremum, then sup E Î E.

True False. If A Í B are nonempty and bounded sets then sup A £ sup B.

True False. The trichotomy property holds in every field.

True False. If A Í B and B is countable, then A is countable.

True False. Every bounded subset of Z has a least element.

True False. Every monotone sequence converges.

True False. The sum of two bounded sequences is bounded.

True False. Every Cauchy sequence is bounded.

True False. If xÎR, then there is a sequence of irrational numbers that converges to x.

True False. The intersection of any sequence of bounded nested intervals is nonempty.

 

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