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Showing posts from March, 2022

Stewart’s Hyperwebster Dictionary, the Sierpiński-Mazurkiewicz Paradox

 In this week's blog post I discuss two paradoxes, Stewart’s Hyperwebster Dictionary and the Sierpiński-Mazurkiewicz paradox, that will help us to understand the Banach-Tarski theorem.

Applying the Axiom of Choice and Infinite Shifts to Demonstrate the Equidecomposability of Incomplete Circles and Spherical Shells

Here is the link to this week's blog, in which we discuss how we can utilize transinfinite point sets to demonstrate the equidecomposability of second and third-dimensional shapes.

Shifting Equidecomposable Point-Sets in First-Dimensional Spaces Towards and From Infinity

Here is this weeks blog on the Equidecomposability of first-dimensional geometry!