Constructing the Reals (Part I) - 14

In this lecture, we begin the process of constructing the reals as a completion of the rationals using Cauchy sequences. We will use this construction to prove a few key theorems about the reals, including that it satisfies the least upper bound property.

Note: there is no pre-lecture video or reading for this lecture. Instead, make sure to review equivalence relations from Module 1.

Reading: Not in Rudin (but a different construction is provided in Ch. 1 Appendix)

Pre-Lecture Materials

In-Class Activities

Open the following Overleaf link and make a copy for yourself. Remember to include the names of everyone who worked together in the document.

Lecture 14 In-Class Activity - Constructing the Reals (Part I) - Equivalence of Cauchy Sequences

Lecture 14 In-Class Activity - Constructing the Reals

Assignments

  • Submit Overleaf Proof 14: Constructing the Reals (Part I)

Additional Materials

Lecture Notes