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I read a formulation like:

"The function $f(x)$ approaches its limit value of $2$ algebraically."

So I'm wondering what's the mathematical equivalant definition of "approching a limit algebraically". In other words, what do I have to show to prove that statement?

MeLoco
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  • I'm assuming it must mean that your function is a sum/difference/product/quotient. See:https://en.wikipedia.org/wiki/Limit_of_a_function#Properties – John11 Sep 02 '16 at 20:30
  • Could you give us some context? – xyzzyz Sep 02 '16 at 20:30
  • Unfortunately not so much,only so far as I can say, that there are functions $f_n$ defined on some compact intterval $[0,n]$ and the function $f$ should be defined as the limit $f:=\lim_{n\rightarrow\infty}f_n$ and every $f_n$ satisfies $f_n(n)=2$. So obviously it makes sense that $f$ reaches the value $2$ for $s\rightarrow\infty$. Only "algebraically" confuses me. – MeLoco Sep 02 '16 at 21:31
  • Maybe there could be a distinction in "algebraically" and "exponentially"? Is there a noticeable difference? – MeLoco Sep 03 '16 at 19:59

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