Ordered Fields
In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms.
Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0
COOL Construction of R (with sequences): https://youtu.be/QiNEdiJAeSg
Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh