# Lecture - Analysis MT22, VIII

### Flashcards

Suppose $\exists k \in \mathbb{N} \text{ s.t. } a _ n > 0$ for $n \ge k$. What is true if and only if $\frac{1}{a _ n} \to \infty$ as $n \to \infty$?

Suppose $\exists k \in \mathbb{N} \text{ s.t. } n > k \implies a _ n = -b _ n$ for $n \ge k$. What is true if and only if $b _ n \to \infty$?

What is the technical definition of $a _ n = O(b _ n)$?

What’s the technical definition of $a _ n = o(b _ n)$?

What does it mean for a sequence $(a _ n)$ to be monotonic increasing?

What does it mean for a sequence $(a _ n)$ to be monotonic decreasing?

What does it mean for a sequence $(a _ n)$ to be monotonic?

If it is monotonic increasing or monotonic decreasing.

What is the monotonic sequence thoerem about an monotonic increasing sequence $(a _ n)$?

What key idea is there that you use to prove the monotonic sequence theorem?

Using the completeness axiom.