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by joe_the_user
2380 days ago
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That is certainly how I would understand the situation. However, it seems intuitively you construct the notion of finite, could engage in the ordinary computation and have a way of distinguishing these "weird roots" from regular roots. I suppose if you make the position of (something like) "every polynomial whose root cannot be found by finite calculation does not, in fact, have one" an axiom but then you would have discarded the notion of finite axioms (you'd have a second order system). Still, might actually have a way to specify "truth", something I'd thought was a bit beyond logic at this point. |
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