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## Algebraic numbers as sequences… [closed]

Is a number algebraic iff it can be written as the limit of a sequence of the form $\langle \frac{an + b}{cn + d} \rangle_{n \in \mathbb{N}}$ where $a, b, c$ and $d \in \mathbb{Q}$ are constants.

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I don't understand the question. – Igor Rivin Dec 1 2011 at 15:57
Igor what don't you understand? – George Lazou Dec 1 2011 at 16:02
@George Lazou: What you wrote down is not a sequence. Do you mean that $a, b, c, d$ stay constant and $n$ runs through the positive integers? If so, please say it. – Igor Rivin Dec 1 2011 at 16:07
I'm sure Igor understands what the words mean and what the question says. But maybe he wants to know why you are asking it. Do you already know one direction? Do you have any evidence for thinking this is true? What were you doing when you thought this question? Things like that would help. – Francis Adams Dec 1 2011 at 16:08
If, as Igor guessed, $a,b,c,d$ are supposed to remain constant while $n$ increases, then the limit is $a/c$, hence not only algebraic but rational. If, on the other hand, $a,b,c,d$ are allowed to depend on $n$, then every real number occurs as such a limit. Either way, it isn't a research-level question, so perhaps something else was intended --- but what? – Andreas Blass Dec 1 2011 at 16:12