As I don't know what theorem 9 tries to say, I can't follow the highlighted statement in the proof of theorem 14. Could you please help explain theorem 9 in plain English to a layman like me, and why it leads to that statement d + e <= e?
2026-04-02 08:53:45.1775120025
The meaning of theorem 9 (Set Theory and Metric Spaces - Kaplansky)
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A partial ordering is a binary relation which reflexive, anti-symmetric and transistive. What matters here is that it is anti-symmetric: if $e\leqq d+e$ and if $d+e\leqq d$, then $e=d+e$.