Maths Major - Blog Posts
Heya!!
Today I revised some stuff (90% of the day lol) and did chapter 10.Chapter 10 is about the scenic viewpoint theorem,Bolzano-Weierstrass theorem for real and complex numbers.
Fun fact: Bolzano- Weiestrass theorem for reals makes use of the scenic view point theorem and monotonic sequence theorem but both of them are not valid in the complex numbers because complex numbers don't have order.
This chapter also discussed about Cauchy sequences (it has to satisfy a condition to be called that),some facts (and proofs!) about when it is bounded and such and finally the Cauchy convergent criteria.
I also did chapter 11.It is about the convergence of series.It initially told me what series means and some popular series ( telescoping,harmonic,geometric etc) and what do we mean when we say a series is convergent.It spoke about some nice theorems (involving series of non negative terms,comparison test,cauchy criteria,absolute convergence) and some examples based on the theorems.I did get one basic doubt and I'm sure my friend will be able to clear that out as well.He really has my back when it comes to these silly doubts ^_^