Fields, Order, and Bounds - 3

So far we’ve met some interesting infinite sets, including the natural numbers, the rationals, and the reals. In this lecture, we’ll explore some structural and algebraic properties that these sets have. How are they similar, and how are they different? What is it that makes the real numbers so special?

Reading: Rudin Chapter 1: Ordered Sets, Fields, The Real Field, The Extended Real Number System, The Complex Field, Euclidean Spaces (pgs. 3–17)

Pre-Lecture Materials

Order, Fields, and Ordered Fields: Pre-lecture video A

Upper Bounds, Supremum, and the Axiom of Completeness: Pre-lecture video B

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 3 In-Class Activity: Archimedean Property

Assignments

  • Submit your Overleaf proof 03: Archimedean Property
  • Homework 2

Lecture Notes