PONS OpenDict
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Of course, this collection would have to satisfy certain properties (known as axioms) for otherwise we may not have a well-defined method to measure distance.
en.wikipedia.org He has worked on reverse mathematics, a project intended to derive the axioms of mathematics from the theorems considered to be necessary.
en.wikipedia.org The resulting structure, a model of elliptic geometry, satisfies the axioms of plane geometry except the parallel postulate.
en.wikipedia.org This produces two different lines through a point both parallel to another line, contradicting the axiom.
en.wikipedia.org Accepting only the axiom schema of specification was the beginning of axiomatic set theory.
en.wikipedia.org