This week we defined the set of real numbers more formally by discussing Dedekind cuts. I demonstrated some proofs of properties of the real numbers, including addition, multiplication, ordering, and completeness. Week_12___One_Way_to_Construct_the_Real_Numbers
Week 11 – Sequences of Functions
This week I researched pointwise and uniform convergence but got stuck trying to prove convergence of the Taylor Series for sin(x).
Week_11___Sequences_of_FunctionsWeek 10 – Cauchy Sequences
This week I continued with proofs related to Cauchy sequences, specifically relating the sequence to series convergence and proving that a sequence is not a Cauchy sequence.
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Week 9 – Cauchy Sequences
Professor Davis presented an interesting and, to my understanding, somewhat unorthodox way of constructing the real numbers using a mathematical idea called a Cauchy Sequence. This week, I worked on proofs involving these Cauchy sequences.
Week_9___Cauchy_Sequences_and_Real_Numbers