Why is this set determined to be empty? From Eccles' Introduction to Mathematical Reasoning, problem 7.1 asks you to determine the set for:
$${\{n \in \mathbb{Z}^+ \mid \forall m \in \mathbb{Z}^+, m \leq n \}}$$
The answer provided in the back of the book is $\emptyset$. Why is $\{1\}$ not an answer? It satisfies $\mathbb{Z}^+$ and $m \leq n$, does it not?

In your question, m is an arbitrary integer. You are going to pick an integer n which satisfying the condition for all m belongs to Z, m <=n.
If you are choosing n=1 then it fails for m=2.
So we come to know that there is no such integer n.
Thus the set having no elements.
Empty set.
