3 ms·
That is a great paper. I came up with my own definition of real numbers [1] and using the simplified cut property of that paper was a pleasant pathway to establ
by jostylr 2y ago
That is a great paper. I came up with my own definition of real numbers [1] and using the simplified cut property of that paper was a pleasant pathway to establishing completeness.
[1]: https://github.com/jostylr/Reals-as-Oracles/blob/main/articles/rational-betweenness-relations-oracles.pdf https://github.com/jostylr/Reals-as-Oracles/blob/main/articl...
- fjfaase 2y agoHow does this compare to the surreal numbers defined by Conway?
- jostylr 2y agoAs far as I can tell, they are unrelated beyond the relation all definitions of real numbers would have with it. There is a superficial Left and Right boundary defining an interval that contains the number, but it does not seem like there are a family of intervals for a given real number in this approach. I do not get the feeling that there is a narrowing down to a given number in the surreal numbers, but I know very little about them. I also do not immediately see how my construction could be extended to infinitesimals or the infinite numbers.