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?

Is $1\geq m$ for every positive integer $m$? In words, the set is the set of all positive integers greater than or equal to all positive integers.
