Unsolved problem [entries|reading|network|archive]
simont

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Wed 2014-02-19 10:52
Unsolved problem
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[personal profile] jackMon 2014-03-10 13:14

I now actually read this proof, and it sounds right to me, though I don't guarantee I haven't missed some exception.

What confused me in the pub is, you use the axiom of choice to get a basis for R over Q. But don't you just need a basis over Q for the vector space generated by the fragment lengths you actually have, not over any possible irrationals? Isn't that just some subset of the fragment lengths, throwing away any non-linearly-independent ones?

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[personal profile] simontMon 2014-03-10 13:33

Ah! Yes, good thought. And that vector space is finite-dimensional, because we have at most finitely many frag lengths, and hence we don't need AC to conclude that it has a basis. Well done.

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