Hilbert's Discarded Axiom
Hilbert (1899) included a 21st axiom that read as follows:
- II.4. Pasch's Theorem. Any four points A, B, C, D of a straight line can always be so arranged that B shall lie between A and C and also between A and D, and, furthermore, that C shall lie between A and D and also between B and D.
E.H. Moore and R.L. Moore independently proved that this axiom is redundant, and the former published this result in an article appearing in the Transactions of the American Mathematical Society in 1902.
Read more about this topic: Hilbert's Axioms
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