Posts

Showing posts from February, 2022

The Independence of the Axiom of Choice From Zermelo-Fraenkel Set Theory (ZF)

 Here is the link to my blog post.   This week we will finish discussing the prerequisite set theory necessary to understanding the Banach-Tarski Theorem.

Implications of the Axiom of Choice Within Set Theory

Here is the link to this week's blog post! I did not have the time to write about everything I planned to this week, but hopefully next week I can finish the discussion of set theory and move on to the geometry of the Banach-Tarski theorem.

The Incompleteness Theorems and Their Relevance to Axiomatic Indeterminance

Here is the link to the Google Document for this week's blog post. Unfortunately I am still unable to upload to Blogger due to the lack of support for mathematical notation. 

Research Proposal For the Study of Transinfinant Sets as They Relate to the Banach-Tarski Theorem

Unfortunately, Blogger is making it very difficult for me to retain the formatting of the mathematical notation in my writing when using their client. Due to this I will be hosting my blogpost for this week on Google Docs at this link while I work to find a longterm solution to this issue. I have enabled commenting on the document. I apologize for any inconvenience.