Axiomatics and the least upper bound property (I) | Real numbers and limits Math Foundations 120

Описание: The role of axiomatics in mathematics is a highly contentious one. Originally the term always referred to Euclid, and his use of the term to mean `a self-evident truth that requires no proof '. However in modern times the meaning of the term has shifted dramatically, to the idea that an Axiom is `a convenient fact that we assume'.

This casts considerable doubt on the validity of the usual claim that `Mathematics is built on Axioms", which these days appears more and more as a religious position rather than a scientific one. Is that what we want our subject to be?? Your belief system as opposed to my belief system??

In this video we discuss this shift in meaning and its consequences when trying to set up a theory of real numbers. We will be discussing this important issue further when we get around to critiquing `modern set theory'.

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