Nonstandard Integers as Complex Numbers

 

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I just read something cool:

• Joel David Hamkins, Nonstandard models of arithmetic arise in the complex numbers, 3 March 2018.

Let me try to explain it in a simplified way. I think all cool math should be known more widely than it is. Getting this to happen requires a lot of explanations at different levels.

Here goes:

The Peano axioms are a nice set of axioms describing the natural numbers. But thanks to Gödel’s incompleteness theorem, these axioms can’t completely nail down the structure...