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Construction of the Real Numbers

Dedekind Cuts In this video, I rigorously construct the real numbers from the rational numbers using so-called Dedekind Cuts. It might seem complicated at first, but the advantage is that we can construct the real numbers without using any axioms. More importantly, in the next video, we use this to easily prove the least upper bound property. Enjoy! Least Upper Bound Proof:    • Least upper bound proof   Cauchy Construction of R:    • Real numbers Cauchy construction   Axioms of R:    • What is a real number?   Check out my Real Numbers Playlist:    • Real Numbers   Check out my Set Theory Playlist:    • Set theory