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I happen to be reading Poincare's Science and Hypothesis right now and he introduced a way of defining the square root of two that I found enlightening. In less
by diffxx 2y ago
I happen to be reading Poincare's Science and Hypothesis right now and he introduced a way of defining the square root of two that I found enlightening. In less articulate form: consider two sets, one of which contains all numbers whose square is less than two and one of which contains all numbers whose square is greater than two. The square root of two is then the symbolic name for the element that divides those two sets.
Poincare says it better in the book though.
- __MatrixMan__ 2y agoI think you're describing a https://en.wikipedia.org/wiki/Dedekind_cut https://en.wikipedia.org/wiki/Dedekind_cut (edit: oh, I see the article makes that clear. Well here's a link anyway)
- postoplust 2y agoThat's also the definition given in the article, attributed to Richard Dedekind.
- deleted 2y ago[deleted]
- andoando 2y agoYou can do the same with all numbers, and you get the construction of the surreal numbers.