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The measure of epsilon is 0. Proof: what else could it be? If it's not 0, there's a smaller number, contradicting your (intuitive) definition of epsilon.
by gertef 9y ago
The measure of epsilon is 0.
Proof: what else could it be? If it's not 0, there's a smaller number, contradicting your (intuitive) definition of epsilon.
- CuriouslyC 9y agoWouldn't it be more accurate to describe epsilon as an infinitesimal?
- alexbecker 9y agoThere 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 9y agoInteresting. How do you describe the difference between two successive real numbers?
- stymaar 9y ago> How do you describe the difference between two successive real numbers? There is no such things as «two successive real numbers».
- alexbecker 9y agoYeah, there aren't even two successive dual numbers. What's after 1? If it's 1 + epsilon, then what about 1 + epsilon / 2?