Definition of Axiom

Topic 2 of "Brief Introduction to the Foundations of Mathematics" lecture.

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In this video we will define Axiom and talk briefly about why it is different from a Postulate.

In addition, we will review the concepts of Theorem, Lemma, and Corollary.

Finally, we'll talk about the enormous importance of axioms as the foundation for the development of Scientific Theories.

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[john_g_harris]

It's better to say that axioms are just rules that are true in some cases and false in other cases. It is humans who assume they are true for the subject they are talking about. They might be wrong.



For instance, the subject might be simple addition. It obeys the axioms of group theory so the axioms can be used to deduce things about addition. But if the subject is horse racing then the group axioms are not obeyed so assuming them to be true would be a big mistake.

[MaxCoplan]

This voice is awful. Would have liked it if we could've heard a real voice