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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
awarded  Revival
Sep
20
comment Look at the following infinite sequence: 1, 10, 100, 1000, 10000, . . ..
@Olcayto‌: Any number and any sequence. :-)
Sep
17
awarded  Good Answer
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.
Aug
9
revised Where did $-4x$ come from?
removed stray +4
Aug
9
revised Where did $-4x$ come from?
removed stray +4
Aug
4
awarded  Good Answer
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
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 On the Origin and Precise Definition of the Term 'Surd'
Jul
21
comment Is $.\overline{9} = 1$?
@ElazarLeibovich: Yes, that's what I was pointing out. :-)
Jul
20
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 $1/3 = 0.333\dots$.
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