The late Edward Nelson has a number of papers discussing potential and actual infinity on his personal page https://web.math.princeton.edu/~nelson/papers.html

One could look at https://web.math.princeton.edu/~nelson/papers/warn.pdf

]]>There’s a reference to the formula here: https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

It converges quite slowly, but it does indeed converge to π.

]]>It starts with 4 – 4/3. I think you’re reading the subtractions as multiplications?

]]>These remarks by Harold M. Edwards in the introduction to his Divisor Theory may be relevant:

“ … one of Kronecker’s most valuable ideas, namely, the idea that the objective of the theory [of divisors] is to define greatest common divisors, not to achieve factorization into primes.

The reason Kronecker gave greatest common divisors the primary role is simple: they are independent of the ambient field while factorization into primes is not. The very notion of primality depends on the field under consideration–a prime in one field may factor in a larger field- so if the theory is founded on factorization into primes, extension of the field entails a completely new theory. Greatest common divisors, on the other hand, can be defined in a manner that does not change at all when the field is extended … “

]]>(My choice: Work upwards, not downwards. Define a quasigroup as an algebraic object whose operation table is a Latin Square. Now a loop is a quasigroup with an identity.)

Bob W

]]>My observation is that we usually choose the definition of something to suit our present purpose and prove theorems that give equivalent definitions. My current example was choosing an appropriate definition for a module being finitely co-generated.

I look forward to reading your future insights. Mentioning what mathematics is “trendy” or “fundable” was so on point.

]]>It discusses questions related to “what is number” and outlines how the notion of number changed from the Greeks through to the modern period.

]]>And Cov . A is A . Lambda [not Lambda . A] so the

commutation was not necessary. I’ll try to get this corrected. Tony ]]>

BTW, an excellent article!

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