Axiomatics and the Least Upper Bound Property in Real Numbers - Math Foundations 120

Axiomatics and the Least Upper Bound Property in Real Numbers - Math Foundations 120

Explore the evolving role of axiomatics in mathematics and its impact on the theory of real numbers in this thought-provoking lecture. Examine the shift in meaning of the term "axiom" from Euclid's "self-evident truth" to the modern interpretation of "assumed fact." Delve into the consequences of this change when establishing a theory of real numbers and question the validity of the claim that "Mathematics is built on Axioms." Consider the implications of this shift on the scientific nature of mathematics and its potential reduction to competing belief systems. Gain insights into this critical issue, which will be further explored in future discussions on modern set theory.