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> I'm very happy to accept than any length in geometry is a number by definition Interestingly, that set of numbers is still very incomplete relative to what w
by umanwizard 8y ago
> I'm very happy to accept than any length in geometry is a number by definition
Interestingly, that set of numbers is still very incomplete relative to what we expect to be able to talk about in modern math. It doesn't even include the roots of all polynomials (for example, the unique positive solution to x^3 - 2 = 0 isn't the length of any constructible segment in classical geometry).
- nimonian 8y agoWhat does 'in geometry' mean in this context? There are numbers which are not constructible with compass and straight-edge constructible but which are constructible by other means (e.g. 2^(1/3) is origami constructible).
- umanwizard 8y agoThat's why I said "classical geometry" instead of just "geometry" - I meant Euclidean compass-and-straightedge.