Construction of the Real Numbers

Описание: 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