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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 I don't get a 'What if' math joke
@bcrist: Ah I see... I was wrong, thanks for that!
Mar
7
comment I don't get a 'What if' math joke
@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 I don't get a 'What if' math joke
@Ant: what-if.xkcd.com has nothing to do with the xkcd comic either, besides being hosted on the same domain. :-)
Mar
7
comment I don't get a 'What if' math joke
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.
Sep
22
comment The myth of no prime formula?
You ignored the word "useful" in Tao's comment: here, "useful" means something that allows us to compute the $n$th prime significantly faster than what follows straightforwardly from its definintion.
Sep
22
comment Why doesn't the definition of the interior of a set depend on the dimension of the set
The definition of interior does depend on the space you're working in (in exactly the ways you mentioned). What definition have you seen?
Sep
21
comment Is there a known mathematical equation to find the nth prime?
Why the downvote?
Sep
20
comment Look at the following infinite sequence: 1, 10, 100, 1000, 10000, . . ..
@Olcayto‌: Any number and any sequence. :-)
Aug
16
comment Is '10' a magical number or I am missing something?
@JoSo: You may notice that I always used "base 1" in quotes — of course it's not one of the general class of "base n" representations, but there does exist such a thing as the unary numeral system: en.wikipedia.org/wiki/Unary_numeral_system. I feel I'm repeating the comment I made to user dhasanen above. In the unary numeral system, you can use any symbol you like (either 0 or 1 or X or whatever), and correspondingly 0000 or 1111 or XXXX would represent the number 4.
Jul
29
comment Are there more examples of functional equations which are also valid for the identity map?
@Isomorphism: Feel free to edit the question (you can mention Semiclassical in your edit) -- improving the question to make it clearer (and answerable) is very much encouraged, not frowned upon.
Jul
27
comment Are there more examples of functional equations which are also valid for the identity map?
Well, $\sin$ is not a homomorphism, and $\sin (A^2) \neq \sin^2 (A)$ (which stands for $(\sin A)^2$), and the OP explicitly excludes homomorphisms as trivial, so... yeah it's not clear what "preserve" means.
Jul
21
comment Is $.\overline{9} = 1$?
@ElazarLeibovich: Yes, that's what I was pointing out. :-)