I have a question of the likes of: Show that:
$\exists m \in \mathbb{Z}^+, \forall n \in [m,+\infty), 10n^2 +100/n > 0$.
I'm not sure exactly where to and how to start this question. I have a variety of properties in front of me, but I'm not sure how I would go about using them. I know at first I should state "let n be an integer", but then I'm completely lost.
Any help would be much appreciated.
First of all, the Order matter here, so your first thoughts are on the correct path.
The answer is m=1.
Now this is how you prove it. Note that in the inequality n cannot equal 0 because 100/0 is not allowed. so since n cannot equal 0, and m is in the Z+ set , setting m=1 will make the statement true for any value of Y.
Make sense? hope it helps