Question

Prove or Disprove: −N := {z ∈Z : −z ∈N} has the Upper Well Ordering Property.

Answer 1

A set of numbers has the Upper Well Ordering Property if and only if every non empty subset has a greatest element.

Answer 2

Is it not that \(\mathbb N\) itself an uncountable set?

Answer 3

\(\mathbb N\) is natural number, hence \(z \in \mathbb Z| z\in \mathbb N\) is only \(-\mathbb N\) itself --> it is not an Upper well ordering set. (to me)

Answer 4

i didn't get why?
can you please give me an example