If a monotone increasing sequence is not convergent, then is the sequence unbounded?
I know that a monotone increasing sequence that is convergent must be bounded.
But $P \to Q$ being true doesn't necessarily mean $-P \to -Q$ must be true.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
Let $(a_n)$ an increasing and divergent sequence of real numbers.
If we suppose that this sequence has an upper bound, being increasing and having an upper bound, it would converge to some real limit : a contradiction. So this sequence doesn't have any upper bound (and in particular, it's unbounded).