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Rotwang <sg552 at hotmail.co.uk>: >> for x in continuum(0, max(1, y)): >> # Note: x is not traversed in the < order but some other >> # well-ordering, which has been proved to exist. >> if x * x == y: >> return x > > [...] > > More importantly, though, such a computer could not complete the above > iteration in finite time unless time itself is not real-valued. That's > because if k is an uncountable ordinal then there is no strictly > order-preserving function from k to the unit interval [0, 1]. If you read the code comment above, the transfinite iterator yields the whole continuum, not in the < order (which is impossible), but in some other well-ordering (which is known to exist). Thus, we can exhaust the continuum in ?? discrete steps. (Yes, the continuum hypothesis was used to make the notation easier to read.) Marko

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