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There are no infinitesimals in the reals. You can define a mathematical structure containing infinitesimals [0], but it's not the reals. [0] Specifically, the
by alexbecker 10y ago
There are no infinitesimals in the reals. You can define a mathematical structure containing infinitesimals [0], but it's not the reals.
[0] Specifically, the dual numbers: https://en.wikipedia.org/wiki/Dual_number https://en.wikipedia.org/wiki/Dual_number
- CuriouslyC 10y agoInteresting. How do you describe the difference between two successive real numbers?
- stymaar 10y ago> How do you describe the difference between two successive real numbers? There is no such things as «two successive real numbers».
- alexbecker 10y agoYeah, there aren't even two successive dual numbers. What's after 1? If it's 1 + epsilon, then what about 1 + epsilon / 2?