Szpilrajn extension theorem

In order theory, the Szpilrajn extension theorem (also called the order-extension principle), proved by Edward Szpilrajn in 1930, states that every partial order is contained in a total order. Intuitively, the theorem says that any method of comparing elements that leaves some pairs incomparable can be extended in such a way that every pair becomes comparable.

Source: Wikipedia — Szpilrajn extension theorem (CC BY-SA 4.0)

Szpilrajn extension theorem

In order theory, the Szpilrajn extension theorem (also called the order-extension principle), proved by Edward Szpilrajn in 1930, states that every partial order is contained in a total order. Intuitively, the theorem says that any method of comparing elements that leaves some pairs incomparable can be extended in such a way that every pair becomes comparable.

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Source: Wikipedia "Szpilrajn extension theorem" · CC BY-SA 4.0

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