Week 6

Since this week’s classes were spent discussing proof, how to come up with ideas for proving something, and how to get those ideas down onto paper, I decided to forge ahead and start next week’s material by reading ahead in the textbook and taking notes on some key ideas regarding the set of real numbers. This week’s post includes these key ideas, along with a few proofs that I worked on alongside the reading that are most relevant to real analysis.


Week 5

This week, I worked on the proof from the previous week. Upon completion of this proof, I used it to work on proofs for the other exercises for irrational numbers.  For these exercises, based on what we discussed in class, I primarily focused on explaining the concepts necessary to establish the proof, rather than just creating a long list of algebraic manipulations. This week should complete my investigation of the irrational numbers.

Week_5___sqrt_2__and_the_Irrational_Numbers (4)

Week 4

This week I struggled with a proof regarding the convergence of the continued fraction for approximating sqrt(2), finding that statement that the exercise asserted was actually false. Since this proof was required to complete further exercises,  this week’s work is shorter than the previous; I have only included two short proofs this week regarding continued fractions.

Week_4___sqrt_2__and_the_Irrational_Numbers (4)