Here, we investigate a conjecture I have, that all normal numbers are transcendental.
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Category: Math
In this post, we summarize my previous work of the series in a more readable and concise manner. (Proofs are not included.)
In this post, we continue the discussion from the previous in the series.
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An Abstract Approach to Generating Sets 3
In this post, we continue the discussion from the previous in the series.
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A Curious Question on Modular Arithmetic
In this post, we investigate a curious question: say we are given 
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Intro to Semilinear Maps
I first learned about (and actually re-discovered) semilinear maps through one of my mathematical explorations. In this article, we introduce them and prove some basic results about them. We assume some knowledge of abstract algebra and related subjects (vector spaces, modules, universal algebra, category theory, etc.)
(I was still learning more about the concept alongside writing this article, so if there are any inaccuracies here, please let me know!)
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My Thoughts on Teaching Model Theory
I have been realizing recently that many of my math ideas in their “ultimate” forms seem highly suited for formulations in model theory. However, when first trying to study some of the resources I found online for model theory, I didn’t even understand that well what the subject was about or why certain definitions were made, let alone appreciate the overall power of the subject. I think there should be a different approach to teaching model theory, incorporating better motivation and more fully reflecting the incredible power and scope of the subject.
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An Abstract Approach to Generating Sets 2
We continue the discussion from this post.
We continue the discussion from the previous post in the series.
Topologies and measure theory’s sigma-algebras look superficially similar, but the differences in their defining axioms lead to differences in their resulting study. In this post, we write this out to understand this better.