EDB — 289

[289] Let \(n,m,k∈ℕ\).

1. For every \(n\) we have \(0\le n\)

2. \(n≤ m\) if and only if \(n{\lt} S(m)\).

   Note that these two points satisfy [(4.29)]↺↻,[(4.28)]↺↻ in [26H]↺↻

3. For every \(n\) we have \(n{\lt}S(n)\)

4. \(n{\lt}m\) if and only if \(S(n)≤ m\).

5. If \(n≤ m ≤ S(n)\) then \(m=n\) or \(m=S(n)\).

The proofs are left as exercise [28D]↺↻. (After we will prove that the relation is total, then by [26X]↺↻ the last two are equivalent.)