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 that U = Q, unless stated otherwise.


True False. Every bounded monotone sequence converges.

True False. The Squeeze Theorem is still true (even though U = Q).

True False. The Archimedean Principle is still true.

True False. The union of an infinite sequence of bounded sets is bounded.

True False. Every bounded sequence has a convergent subsequence.

True False. Every Cauchy sequence is bounded.

True False. Every convergent sequence is Cauchy.

True False. If two sequences diverge to infinity, so does their sum.

True False. Every nonempty bounded set has a supremum and an infimum.

True False. Every Cauchy sequence with a convergent subsequence converges.

 

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