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 Jun30 comment Does this weird sequence have a limit? @anon: Making a needlessly complicated definition was sort of the point. Also, you don't necessarily have to choose $k$ randomly. You can start from $1$ and work your way up if you want; the point is not so much in what order the terms are calculated, but that you can calculate $a_k$ for any $k$ you want. Jun30 comment Does this weird sequence have a limit? @AndréNicolas: What I mean if that $a_k$ has already been calculated, there is no need to roll the die again. We just look at the list and check what was the value of $a_k$. Jun30 asked Does this weird sequence have a limit? Jun24 awarded Nice Question Jun23 revised Expanding out summation signs transformed image into latex, hope I read it right Jun23 suggested approved edit on Expanding out summation signs Jun23 comment If a function has a finite limit at infinity, does that imply its derivative goes to zero? Also, a nitpick: shouldn't it be $x > 0$ instead of $x \ge 0$? Jun23 comment If a function has a finite limit at infinity, does that imply its derivative goes to zero? This is the answer I like more, simply because you provided a function for which it is easy to check that it's a counterexample (just differentiate and take limits). Thanks! Jun23 accepted If a function has a finite limit at infinity, does that imply its derivative goes to zero? Jun23 asked If a function has a finite limit at infinity, does that imply its derivative goes to zero? Jun20 awarded Nice Question Jun8 awarded Caucus Jun4 accepted How do we know that $\exp(x)$ agrees with raising a number to a rational power? Jun4 comment How do we know that $\exp(x)$ agrees with raising a number to a rational power? Yeah, sorry about that, fixed it. I think I liked Jim Belk's answer a little more, but thanks for your help! Jun4 revised How do we know that $\exp(x)$ agrees with raising a number to a rational power? deleted 168 characters in body Jun4 comment How do we know that $\exp(x)$ agrees with raising a number to a rational power? Yes, we used that property to define rational powers, but we also knew how to define integer powers and roots, and we used $a^{b^c}=a^{bc}$ to define rational powers in terms of those. Jun4 comment How do we know that $\exp(x)$ agrees with raising a number to a rational power? @Limitless: The advanced part is showing that such a function is unique. Wikipedia doesn't give such a proof, and makes some statements that I don't know about, such as the fact that it must be Lebesgue measurable. Jun4 asked How do we know that $\exp(x)$ agrees with raising a number to a rational power? Jun1 accepted Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$ Jun1 comment Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$ That works, then. Don't get me wrong, the rest of your answer is great too, it's just not precisely what I had in mind when I thought of the question. Thanks!