ShreevatsaR
Reputation
25,297
157/100 score
 Jul27 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. Jul25 reviewed Reject On the Origin and Precise Definition of the Term 'Surd' Jul21 comment Is $.\overline{9} = 1$? @ElazarLeibovich: Yes, that's what I was pointing out. :-) Jul20 comment Is $.\overline{9} = 1$? 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 $1/3 = 0.333\dots$. Jul20 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. Jul20 revised How come $32.5 = 31.5$? rolled back to a previous revision Jul13 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. Jul10 awarded Good Answer Jul10 awarded Enlightened Jul10 awarded Nice Answer Jul2 awarded Curious Jul2 comment What five odd integers have a sum of $30$? That is neither 5 numbers nor "summed together". Jun27 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 $n > 2$.) Jun27 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. Jun19 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... Jun18 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.) Jun18 comment Finding Probability of a falling fan Very closely related to this question: Why is not the answer to all probability questions 1/2. Jun17 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! Jun17 comment Blood relation - How A is related to B @Fabien: Why can't A be male (and so A = B)? And how does that fit with the first statement? Jun13 comment Find a generating function for $\sum_{k=0}^{n} k^2$ The sum diverges; also it's a single expression and not a sequence. Perhaps you mean "find a generating function for $\sum_{k=0}^{n} k^2$".