Here, another interesting construction of the real numbers: https://arxiv.org/abs/math/0405454 https://arxiv.org/abs/math/0405454 - The Eudoxus Real Numbers h

Here, another interesting construction of the real numbers: https://arxiv.org/abs/math/0405454 https://arxiv.org/abs/math/0405454 - The Eudoxus Real Numbers https://ncatlab.org/nlab/show/Eudoxus+real+number https://ncatlab.org/nlab/show/Eudoxus+real+number https://en.wikipedia.org/wiki/Construction_of_the_real_numbers#Construction_from_Z_.28Eudoxus_reals.29 https://en.wikipedia.org/wiki/Construction_of_the_real_numbe... (Surprisingly enough, ncat & Wikipedia complement each other here in their explanations of it.)