This is from the Wikipedia entry for Field of Sets

"Fields of sets should not be confused with fields in ring theory nor with fields in physics. Similarly the term "algebra over \(X\)" is used in the sense of a Boolean algebra and should not be confused with algebras over fields or rings in ring theory. "

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It's wild to me that people actually thought naming complex algebras "complex algebras" was a good idea.

I learnt today that the name comes from when subsets of groups were called "complexes", but still...

How prevalent are screen readers with LaTeX support? When I caption images containing equations is it preferable for the captions to be in LaTeX as well? I'm not entirely sure what the alternative would be.

I prefer the term "bounded morphism" over "p-morphism", and " bounded morphism" is the more modern term, but I feel compelled to use "p-morphism" anyway because it happens to be the norm in the subfield my thesis is in.

I came across this nice integerological fact:

Define \(\operatorname{ord}_p(n)\) to be the power of \(p\) in the prime factorisation of \(n\).


\[ \sum_{k=1}^n\gcd(n,k) = \prod_{p|n} \left(1+\left(1-\frac{1}{p}\right) \cdot \operatorname{ord}_p(n)\right) \]

I don't know why you'd want to do this, and all the references I've found to it talk about it as a special case of some more general identities, but for some reason it appealed to me.


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