Every nonempty set of positive integers contains a least element.
This means for the set {a,b} we can determine one of the following to be true:
- a<b
- b<a
Our ability to compare any two values and find which is less than the other allows us to arrange all the values in a progression from lowest to highest.
a < b < c < d < e < f
Appendix A
- {e,b,a,d,c}
- {e,b,d,c} –> a
- {e,d,c} –> a < b
- {e,d} –> a< b < c
- {e} –> a < b < c < d
- {} –> a < b < c < d < e
Rob Sterling 