Set Theory and Logic

   

Confirmation of Playfair's Axiom

Authors: Colin James III

Per "De Morgan that this proposition is logically equivalent to Playfair’s axiom. ... Let X be the set of pairs of distinct lines which meet and Y the set of distinct pairs of lines each of which is parallel to a single common line. If z represents a pair of distinct lines, then the statement, For all z, if z is in X then z is not in Y, is Playfair's axiom, and its logically equivalent contrapositive, For all z, if z is in Y then z is not in X, is Euclid I.30, the transitivity of parallelism." This is confirmed as tautologous.

Comments: 1 Page. Copyright © 2018 by Colin James III All rights reserved. Note that comments on Disqus are not forwarded or read, so respond to this author's email address: info@ersatz-systems dot com .

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Submission history

[v1] 2018-07-29 06:56:29

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