What is a quick way to tell if a series diverges?

A sequence that is bounded but not convergent.

Two series

In your own words, what does it mean if two sets have the same cardinality?

An uncountable set that is a proper subset of

Prove that every convergent sequence is bounded.

A subset of that contains its supremum but not its infimum.

In your own words, what does the Nested Interval Property mean and what axiom does it rely on in its proof?

A sequence such that

Let be the greatest integer less than or equal to . For example,