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1d
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.
2d
awarded  Yearling
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
25
reviewed Reject suggested edit on On the Origin and Precise Definition of the Term 'Surd'
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
20
revised How come $32.5 = 31.5$?
rolled back to a previous revision
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
10
awarded  Good Answer
Jul
10
awarded  Enlightened
Jul
10
awarded  Nice Answer
Jul
2
awarded  Curious
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.