How to show that the following function isn't a polynomial over Q? – mathoverflow.net

How to show that the following function isn't a polynomial over Q? – mathoverflow.net

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Enumerate the rationals as $b_1,b_2,\dots$ and define the (set) function: $$f(x) = (x-b_1)^2 + (x-b_1)^2(x-b_2)^2 + \dots.$$ At any particular $x$, only finitely many terms are non zero so this is ...

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