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Jun
28
comment search on a split data structure
BTW, $b(n)$ is $n$ for the unsorted list as you always need to look at all elements before concluding it isn't there.
Jun
28
comment Special representation of a number
The remarkable resemblance of the two plots is interesting though, and I'm curious what the general shape (of the "upper" and "lower" curves) are.
Jun
28
comment search on a split data structure
It still wasn't clear so I've edited the question; take a look and see if that's what you intended.
Jun
28
comment search on a split data structure
Can you edit the question to make it clearer in the formatting which parts are quotation from the test / homework / question, and which parts are your own thoughts / questions?
Jun
26
comment How many algebras are there of finite-sized $\Omega$?
I just got a notification because this answer was upvoted. Not only do I have no recollection of having posted this answer, I don't even understand it now. At all. Clearly the explanation could have been better!
Jun
26
comment Expectation value of number of drawings of increasing sequences of labelled balls from an urn.
@uomoinverde The bounty doesn't matter so much; what would be gratifying would be if you indicated that you understood the ideas better now. :-)
Jun
26
comment Expectation value of number of drawings of increasing sequences of labelled balls from an urn.
Note that the question asks for the probability that the number of drawings is greater than $k$, but you seem to be calculating $\Pr(X \ge k)$ instead of $\Pr(X > k)$ (which is what it asks for).
Jun
18
comment How to determine growth rate of coefficients of generating function
@Michael Yes, their Chapter VIII on the saddle-point method covers such generating functions.
Apr
15
comment Maximizing profit (dynamic programming)
More precisely: how many of questions up to 18 did you solve? Why attempt 19?
Apr
15
comment Maximizing profit (dynamic programming)
Guess you need to first read about dynamic programming before solving exercises. Did you manage to solve all (or most) of questions 1 to 18, before attempting question 19?
Mar
22
comment Is this 5th root in the set of natural numbers?
What have you tried? What leads you to the belief that no such $x$ exists? If you include that in your question you are more likely to get an answer.
Mar
8
comment “What if” math joke: the derivative of $\ln(x)^e$
@bcrist: Ah I see... I was wrong, thanks for that!
Mar
7
comment “What if” math joke: the derivative of $\ln(x)^e$
@bcrist: Ah good point; perhaps one should say that though the What-If series contains references to the XKCD comics, there is none in the other direction. (Sort of how I can make references to a TV show, but a TV show will never make references to me.) At any rate, the subject of this question definitely doesn't count as "an xkcd", whatever that means. Nor is it even a joke, IMO.
Mar
7
comment “What if” math joke: the derivative of $\ln(x)^e$
@Ant: what-if.xkcd.com has nothing to do with the xkcd comic either, besides being hosted on the same domain. :-)
Mar
7
comment “What if” math joke: the derivative of $\ln(x)^e$
This has nothing to do with xkcd, besides being by the same author.
Jan
23
comment Curious Binomial Coefficient Identity
Just for completeness, on deriving $B(x)$: note that $\sum_{n=0}^{\infty}\binom{n}{k}x^n = \sum_{n=k}^{\infty}\binom{n}{k}x^n = x^k\sum_{n=0}^{\infty}\binom{n+k}{k}x^n =x^k\sum_{n=0}^{\infty}(-1)^n\binom{-k-1}{n}x^n=x^k(1-x)^{-k-1}$ as $$\binom{-k-1}{n} = \frac{(-k-1)(-k-2)\cdots(-k-n)}{n!}=(-1)^n\frac{(n+k)\cdots(k+1)}{n!} =(-1)^n\binom{n+k}{k}.$$
Jan
22
comment Curious Binomial Coefficient Identity
@anorton: Quite clearly from context, $a_n = \binom{n}{k}$ (for some/any fixed $k$).
Dec
7
comment Can I get a decimal number does not contain a similar consecutive double-digit???
Try $12/99 = 0.12121212...$
Nov
29
comment Prime numbers stretch to infinity, but what about the distance between them?
But Zhang's result does prove the "probably" at the top: it proves that $\liminf_{n \to \infty} (p_{n+1} - p_n)$ is finite, and therefore the $\limsup$ and $\liminf$ are different, i.e. the limit definitely does not exist.
Sep
23
comment Does the number pi have any significance besides being the ratio of a circle's diameter to its circumference?
@Ant: My comment was a reply to asmeurer's speculation that it had to do with "angles and the 2D lattice" -- my comment was not a reply to anything in this (damiano's) answer.