Lecture

Real Numbers: Order and Completeness

Description

This lecture covers the properties of real numbers, focusing on the total order and completeness. It explains the Archimedean property, equivalence with the existence of bounds, and the concepts of supremum and infimum. The lecture also delves into the axioms of Archimedes and the implications for irrational numbers. The instructor reviews the definitions of intervals, open and closed sets, and provides examples to illustrate the concepts.

Official source

https://mediaspace.epfl.ch/media/0_505iops9

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Mathematical logic: Set theory

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