1. ## limit proof

Let (x sub n) and (y sub n) be sequences of positive numbers such that
lim(x sub n/y sub n) = 0. Prove if lim(x sub n)= positive infinity, then
lim(y sub n) = positive infinity.

2. Originally Posted by hayter221
Let (x sub n) and (y sub n) be sequences of positive numbers such that
lim(x sub n/y sub n) = 0. Prove if lim(x sub n)= positive infinity, then
lim(y sub n) = positive infinity.
the conditions on the terms of the sequences and:

$\lim(x_n/y_n) = 0$

means that for all positive $\varepsilon$ eventually

$0 < x_n/y_n<\varepsilon$

so:

$x_n<\varepsilon y_n$

and as $x_n$ goes to $\infty$ so must $y_n$.

Now make this argument more formal and fill in the detail

CB