Monthly Archives: August 2020

Associative universal gates

Posted on August 19, 2020 by apgoucher

The Boolean function NAND is famously universal, in that any Boolean function on n inputs and m outputs can be implemented as a circuit composed entirely of NAND gates. For example, the exclusive-or operation, A XOR B, can be written … Continue reading →

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Another two rational dodecahedra

Posted on August 5, 2020 by apgoucher

Since finding one rational dodecahedron inscribed in the unit sphere, I decided to port the search program to CUDA so that it can run on a GPU and thereby search a larger space in a reasonable amount of time. Firstly, … Continue reading →

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Banach-Tarski and the Axiom of Choice

Posted on August 3, 2020 by apgoucher

Tomasz Kania and I recently coauthored a paper about Banach spaces. The paper makes extensive use of the axiom of choice, involving a transfinite induction in the proof of Theorem B as well as several appeals to the fact that … Continue reading →

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