In this post, we continue the discussion from the previous in the series.
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A More Intuitive Variant of a UFD 2
We continue the discussion started in this post.
We continue the discussion from the previous post in the series.
In this post, we attempt to better understand the questions posed in this post and its follow-up by formalizing them generally in the language of universal algebra.
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General Field Applicability to Infinite Sets
In this post, we undertake a more focused investigation into the conjecture that every infinite set can be turned into a field, as stated in this post. (We assume the Axiom of Choice throughout.)
In this post, we continue the discussion from the previous in the series.
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Sine Angle Product Formula 2
In this post, we continue the discussion from a previous post about the existence of a suitable sine angle product identity.
This is part of a series in which we investigate non-standard axiomatizations of various math structures. The previous post in the series was concerned with single equational axioms for equational classes. In this post, we are inspired by a particularly elegant characterization of (abstract) Boolean algebras, and we consider whether similar “Boolean algebra-like” characterizations can be given for other common structures.
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Sine Angle Addition Functional Equation 2
In this post, we continue the discussion from this post, where we investigate the sine angle addition functional equation
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Sine Angle Addition Functional Equation
In this post, we investigate further the sine angle addition functional equation that I introduced in a previous post, Trigonometric Identities as Functional Equations. (See the work done there before reading this post.) Specifically, the question is to find all functions 
