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If you want to seed doubts in your mind about the real numbers, you can get that at: https://arxiv.org/abs/math/0404335 https://arxiv.org/abs/math/0404335 ...
by flubert 9y ago
If you want to seed doubts in your mind about the real numbers, you can get that at:
https://arxiv.org/abs/math/0404335 https://arxiv.org/abs/math/0404335
...as well (skip to chapter 5 for the impatient).
- openasocket 9y agoI'm fully aware of the complexities of real numbers. But I also know they are essential to derive any advanced mathematics. All the normal derivations and definitions of calculus depend on properties unique to the reals. And while it might be possible to re-derive calculus using computable numbers (I'm fairly sure it is, but not completely), a great many results using topology absolutely depend on the properties of the reals that the domain of computable numbers simply don't have.
- pault 9y agoThis is super interesting, thanks! I love articles that dive into the historical context and philosophy underlying important math discoveries. Context is everything!