In this post, we continue the discussion from this post, where we investigate the sine angle addition functional equation
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Author: Nihal Uppugunduri
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Normal Subset of a Group
We attempt to generalize the notion of “normal subgroup,” used in studying kernels and homomorphisms, to a “normal subset” that does not have the requirement of being a subgroup, and we see whether it is possible for a normal subset to exist that is not a normal subgroup.
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On the Philosophical Foundations of ZFC
In this post, we discuss some questions concerning the philosophical foundations of ZFC.
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On the Definition of Mathematical Rigor
My philosophical post on the circularity of mathematics implies that formal logic must rest ultimately on an informal foundation. In this post, I discuss what that means for our definition of mathematical rigor, which will be an important reference for future philosophical discussions.
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On Bijections and Isomorphisms
We list some facts concerning bijections and isomorphisms between algebras for my learning (“algebra” in the universal algebra sense here, not the specific vector space based algebraic structure.)
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Definition of a Plane in Three Dimensions
Intuitively, a plane is a flat surface that extends infinitely in all directions. How can we interpret this definition in a formal way, and in particular use that discussion to derive the standard equation of a plane?
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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 
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Interpretations of Model Theory
A typical definition of model theory is “universal algebra plus relations.” However, the term “model” in natural language can typically be used quite generally, especially if we consider how people typically understand its meaning for designing and developing any kind of system. Thus, we could guess just based off terminology that in mathematics, a “model” could be defined, as generally as possible, basically as an “example” (set plus interpretation function) that satisfies any given set of axioms. Is this equivalent to the traditional formulation of model theory? In other words, does the traditional formulation of model theory capture the most general kinds of axioms that an “implementation” could satisfy?
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Topology as an Algebraic Structure 2
In this post, we continue the exploration started in Topology as an Algebraic Structure.
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Topology as an Algebraic Structure
Can we express the axioms of topology equivalently as the axioms of an algebraic structure?
