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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 $.999999999… = 1$?
@ElazarLeibovich: Yes, that's what I was pointing out. :-)
Jul
20
comment Is $.999999999… = 1$?
@frogeyedpeas: It's not that "the asker was implying a limit"; it's that the notation $0.9999\dots$ itself implies a limit, by standard mathematical convention — and there is nothing else other than a limit that it can reasonably mean. (E.g. if $0.9999\dots$ stands for a specific number, then under any reasonable system of notation, the number it stands for is identical to $1$.)
Jul
20
comment Is $.999999999… = 1$?
BTW, the first sentence referring to "all the above answers" does not apply (and has not applied for most of the time this answer has been up), because (in the default view at least) none of them assume that $1/3 = 0.333\dots$.
Jul
20
comment How come $32.5 = 31.5$?
@pushpen.paul: Please don't edit answers unnecessarily, and please don't allege "problems" simply because you may have different preferences. There is no requirement on this site to use math markup everywhere (it's enough to be readable; I have already used math mode in the answer where it was absolutely necessarily), and certainly no requirement to use American spellings.
Jul
13
comment How can I understand and prove the “sum and difference formulas” in trigonometry? (cos(a ± b) = …, etc.)?
@Assad: If I remember correctly, I used TikZ, and this was in fact my first time using TikZ. I wish I had kept the source code of this figure; I haven't used TikZ much since then, and I'd have to re-learn it if I wanted to draw this again from scratch. :-) But it couldn't have been too hard, because I did learn enough to draw this.
Jul
2
comment What five odd integers have a sum of $30$?
That is neither 5 numbers nor "summed together".
Jun
27
comment How to tell if a Fibonacci number has an even or odd index
Yes, as I see it, the question is how efficient doing that is, and whether that's the most efficient method possible. See MJD's answer (which IMO is not complete yet). (BTW, the OP does mention the $F_1 = F_2$ exception, and is presumably fine with a rule that applies only for $n > 2$.)
Jun
27
comment How to tell if a Fibonacci number has an even or odd index
I think the part "compute the index of the Fibonacci number" is what the question is about.
Jun
19
comment Intuitively, what separates Mersenne primes from Fermat primes?
@pew: The "random" heuristic is a very powerful one, coming from the deep and profound prime number theorem. With appropriate modifications, it is consistent with all results proved so far about prime numbers. See for instance here, here, here...
Jun
18
comment Intuitively, what separates Mersenne primes from Fermat primes?
@PedroTamaroff: $2^n + 1$ is prime only when $n$ is a power of $2$. And $2^n - 1$ is prime only when $n$ is a prime numer. So the Mersenne primes are precisely those primes of the form $2^n - 1$, and the Fermat primes precisely those of the form $2^n + 1$. (This is differnet from a hypothetical like "primes of the form $n$", as that would include more primes.)
Jun
18
comment Finding Probability of a falling fan
Very closely related to this question: Why is not the answer to all probability questions 1/2.
Jun
17
comment Blood relation - How A is related to B
Actually, because B's mother is D, it means that A's mother is also D. Definitely something wrong with the problem statement, hopefully!