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dlthomas comments on Beautiful Math - Less Wrong
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Comments (35)
Your procedure (though not necessarily your result) breaks for e^x
Really for non-polynomials, and I think that was implied by the phrasing.
I agree that it's implied by working out the logic and finding that it doesn't apply elsewhere. I disagree that it is implied by the phrasing.
doesn't seem to restrict it, and though I suppose
implies that there is a "maximum exponent in the formula" and with slightly more reasoning (a number of iterations isn't going to be fractional) that it must be a formula with a whole number maximum exponent, I don't see anything that precludes, for instance, x^2 + x^(1/2), which would also never go constant.
Sorry, I was using the weak "implies", and probably too much charity.
And I usually only look at this sort of thing in the context of algorithm analysis, so I'm used to thinking that x squared is pretty much equal to 5 x squared plus 2 log x plus square root of x plus 37.