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The mathematical expression of the mathematical constant $e$ in terms of a limit that goes to infinity is $$e = \lim\limits_{n\rightarrow \infty} \left(1+\frac{1}{n}\right)^n$$

But can we express the mathematical constant $e$ in terms of a limit that goes to zero; $e=\lim\limits_{n\rightarrow 0} ...$?

Thank you.

(problem from book of Spivak)

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    $\begingroup$ Do you $$\lim_{x\to a}f(x)=\lim_{h\to\frac1a}f\left(\frac1h\right)$$? $\endgroup$ – lab bhattacharjee Dec 30 '13 at 15:02
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Is this what you want? $$\lim_{n\to 0}(1+n)^{1/n}=e$$

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  • $\begingroup$ But is it true? $\endgroup$ – user118288 Dec 30 '13 at 15:00
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    $\begingroup$ Yes, it is true. $\endgroup$ – mathlove Dec 30 '13 at 15:00
  • $\begingroup$ Love you man!! thanks!! $\endgroup$ – user118288 Dec 30 '13 at 15:01
  • $\begingroup$ You are welcome! I like your question. $\endgroup$ – mathlove Dec 30 '13 at 15:02
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    $\begingroup$ @Adobe: Thanks. I didn't know that. $\endgroup$ – mathlove Dec 30 '13 at 15:09

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