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.
Category: Math
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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.)
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Algebra of Color Mixing
We consider how we can do algebra with colors. In other words, if we take the set of all colors, what algebraic structures can it be endowed with? In this post, we look at the algebra of color mixing: what is the structure of the algebra that is induced by the operation of color mixing? (What properties does color mixing satisfy?)
In this post, we continue the discussion from the previous in the series.
We can think of modular arithmetic as amending operations on Z to “wrap around and stay in Zn.” Can we generalize this idea to arbitrary groups, or even general algebras?
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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.
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Sequence Containment-Type Results
Let 
Can we make this analogy a bit more precise?
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Teaching Math Can Lead to New Research
I have recently found a curious phenomenon in which teaching math can actually lead to new mathematical ideas, and as a result possibly new research. In this post, I’ll discuss some ways this can happen.
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.
This is the first post in a series. This started as an investigation of various non-standard axiomatizations of common structures, but soon the posts ended up focusing on a particular such kind of axiomatization. Thus, this title is misleading (and anyway, it seems too broad for a single series.)
