Data Structures Theory and Quantifier Expressions Confusing

Question

I have questions on an assignment that want me to show things such as:

$∃m∈Z+,∀n∈m..+∞, 5−100/n > 0$

I am having a hard time grasping the concepts around how to "show" this.

Trying to convert it to plain English I have something like this:

"There exists a positive integer $m$ for every positive $n$ to infinity that satisfies $5-100/n > 0$"

If I am interpreting the question correctly that is step one, however from there I am really confused conceptually what to do and what is required. How can I show this?

Answer 1

With $n=1$ : $100/n=100/1=100$ and $5-100 < 0$.

With $n=20$, we have $100/20=5$ and thus : $5 - 5 = 0$.

But for $n > 20$ we have that $100/n < 5$, and thus $5 -100/n > 0$.

Thus, it is true that :

exists $m \in \mathbb Z_+$ such that : for all $n > m$ :

$5 - \frac {100} n > 0$.