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Jun
30
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 $a_k$.
Jun
30
asked Does this weird sequence have a limit?
Jun
24
awarded  Nice Question
Jun
23
revised Expanding out summation signs
transformed image into latex, hope I read it right
Jun
23
suggested approved edit on Expanding out summation signs
Jun
23
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 $x \ge 0$?
Jun
23
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!
Jun
23
accepted If a function has a finite limit at infinity, does that imply its derivative goes to zero?
Jun
23
asked If a function has a finite limit at infinity, does that imply its derivative goes to zero?
Jun
20
awarded  Nice Question
Jun
8
awarded  Caucus
Jun
4
accepted How do we know that $\exp(x)$ agrees with raising a number to a rational power?
Jun
4
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!
Jun
4
revised How do we know that $\exp(x)$ agrees with raising a number to a rational power?
deleted 168 characters in body
Jun
4
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.
Jun
4
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.
Jun
4
asked How do we know that $\exp(x)$ agrees with raising a number to a rational power?
Jun
1
accepted Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
Jun
1
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!
Jun
1
comment Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
I guess I was looking for answers that use mostly the definition of a limit together with some of $e^x$'s properties, but I'm not sure that's practical.