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Euclid's theorem that there are infinitely many prime numbers has multiple proofs, ranging from Euclid's original theorem that constructs a new prime from a finite list of such, to Euler's proof that ...

Begin with a bit of notation. Let $t = t_0, \ldots, t_d$ be a finite sequence of real numbers. Define $$\lambda^t(x) = x^{t_0} \log(x)^{t_1} \log(\log(x))^{t_2} \cdots.$$ for all real numbers $x \in ...

In the thread Even Xor Odd Infinities I defined odd models of Modular Arithmetic (MA) as models satisfying the axioms of MA and two first order statements. Even XOR Odd Infinities? $O1) \forall x(x=0 ...