EDB — 28B

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Proposition 39

[28B] \(≤\) is an order relation.

Proof

Reflexive property: \(n+0=n\). Antisymmetric property: if \(n+k=m\) and \(m+h=n\) then \(n+k+h=n\) therefore by cancellazione [27V] \(h+k=0\), and for [27W] \(h=k=0\) so \(n=m\). Transitive property: if \(n+k=m\) and \(m+h=p\) then \(n+k+h=p\).

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