Rory O'Kane
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Next privilege 250 Rep.
 Oct20 awarded Necromancer Dec4 comment $x$, $y$, $x+y$ and $x-y$ are prime numbers. What is their sum? I didn’t understand this question until I looked at the answers below. I thought the answer was “$3x+y$, obviously”. But now I see that you are looking for an actual number as an answer. The answers below show that there is only one set of values for $x$ and $y$ that makes the four integers positive and prime, so the actual work of the question is “what are the (only possible) values of $x$ and $y$?”. You’re saying you answered that question by brute-force guessing, but you want to know how to answer it with mathematical reasoning. Nov14 revised How could we solve $x$, in $|x+1|-|1-x|=2$? improve wording of description of some steps Nov14 comment How could we solve $x$, in $|x+1|-|1-x|=2$? I can confirm Bill Dubuque’s comment. I continued working through this approach and ended up with $0=0$. Nov14 answered How could we solve $x$, in $|x+1|-|1-x|=2$? Nov14 revised How could we solve $x$, in $|x+1|-|1-x|=2$? fixed spelling/grammar/typography, improved wording, linked to another relevant plot, explained “CW” Nov14 revised How could we solve $x$, in $|x+1|-|1-x|=2$? fixed typo in final answer “[1,∞[”, wrote out steps of third case like the first and second cases Nov14 suggested approved edit on How could we solve $x$, in $|x+1|-|1-x|=2$? Nov14 comment Maximum of the difference (Though I don’t understand this explanation, its general solution at the end gives solutions for $f_1$ through $f_{10}$ that match the solutions given by my brute-force solver. So that general solution is probably correct.) Nov14 comment Maximum of the difference … I think your explanation would be clearer if it were written with different notation. You could use function notation (change $x_k$ to $d(x, k)$), or you could expand $x_k$ into $(n-k)$ if your new notation is just for conciseness. Nov14 comment Maximum of the difference I’m confused by your notation – I think you’ve overloading subscript too much. Inside your definition of $f$, I thought that the $x_1$, $x_2$, etc. were just numbered placholders. But in the first paragraph, you seem to define a new meaning of subscript. When you define $x_k$, are you defining a new notation, or are you claiming that $x_1$, etc. in your definition of $f$ always follow that pattern? And does your definition of $x_k$ apply to terms like “$n_4$”, or does the first variable have to be $x$? … Nov13 revised Maximum of the difference corrected Big O of maximumValuesForSetsUpTo – O(n*n!) = O(n^2*(n-1)!) = O((n-1)!) = O(n!) Nov13 answered Maximum of the difference Nov13 comment How to convince a layman that the $\pi = 4$ proof is wrong? Further reading: Euclidean distance and taxicab distance. Nov13 awarded Excavator Nov13 comment Is value of $\pi = 4$? Wikipedia links explaining some concepts mentioned here: calculus and (numerical) analysis (classes). Riemann sum. limsup (limit superior). Nov13 revised Is value of $\pi = 4$? replaced \sim(ilar order of magnitude) with \approx(imately equal); improved spelling, grammar, typography Nov13 suggested approved edit on Is value of $\pi = 4$? Nov13 comment Why is $\sqrt{8}/2$ equal to $\sqrt{2}$? To clarify what the edit to the question was: the question originally asked, incorrectly, why $\sqrt{8}/2$ is equal to $\sqrt{4}$. Now it correctly asks why $\sqrt{8}/2$ is equal to $\sqrt{2}$. Nov13 awarded Editor