The Handy Math Answer Book

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Foundations of Mathematics

Axiomatic System

What are some simple examples of axioms?

There are some very basic assertions when it comes to axioms. The following lists only a few classical axioms:

  • Things which are equal to the same thing are also equal to each other.
  • If equals be added to equals, the wholes are equal.
  • If equals be subtracted from equals, the remainders are equal.
  • Things that coincide with one another are equal to one another.
  • The whole is greater than the part.