• Announcements: Today's lecture is slightly longer than most, since we discuss in some detail many axioms and their logical consequences (which you are likely familiar with only in an intuitive and non-rigorous way). These axioms and their consequences will be used in very essential ways throughout the semester -- so please go through them carefully, even if they already look familiar to you. As always, if you have any questions, I am available to answer them in office hours and via email! Have a great rest of your week!

• Video 1: Definition of field. Download file or watch below

• Video 2: Definition of ordered field and some consequences. Download file or watch below

• Video 3: Proofs of some of the consequences of the axioms for field and ordered field. Download file or watch below

• Video 4: Absolute value and the triangle inequality. Download file or watch below

• Video 5: Definition of lower and upper bounds, Sup, and Inf. Download file or watch below

• Video 6: Completeness axiom and definition of $\mathbb R$. Download file or watch below