Ben Alpert
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 Apr10 comment How can you prove that the square root of two is irrational? If $p = 2^k m$ where $m$ is odd, then $p^2 = 2^{2k} m^2$ (where $m^2$ is still odd). Dec2 comment Kleene Closure and determining whether a string x is in a set @BrianM.Scott Oops, my bad. I somehow missed the first paragraph and only read the third. Dec2 comment Kleene Closure and determining whether a string x is in a set For the first set, you could also use a parity argument on the length of the string. Jul13 comment Can two sets have same AM, GM, HM? Very nice solution. Sep19 comment Mandelbrot-like sets for functions other than $f(z)=z^2+c$? @Isaac: Many of your pictures seem to be missing now… Jun27 comment Choose K items from N in a circle No problem, hopefully now it's a little easier to understand! Jun23 comment Use of “inverse” to mean reciprocal Yes, I understood that the reciprocal is a type of inverse, but "inverse" seems overly general to specify a reciprocal relationship. Jun22 comment Finding $\sin(4a)$ if we know $\cos a$ Please ask your second problem as an entirely new question instead of as an edit to this one. Jun21 comment Proving Stewart's theorem without trig Thanks, your answer is definitely good enough for my purposes. Good night! Jun21 comment Proving Stewart's theorem without trig Very nice, thanks! May15 comment Function $F$ that $F(x)+F(-x)=\lim_{y\rightarrow\infty}F(y), \forall x \in \mathbb{R}$ @Tim: Might want to change the title too. May10 comment Calculate intersection of 2 points @J.M. I'm pretty sure Ross Millikan interpreted it right. You have two points and two slopes given as angles from the vertical ($\pi/2$) and want the intersection between the two lines thus determined. Apr28 comment Why the name 'FACTORIAL'? But that's true of other numbers (both smaller and larger) that aren't the factorial. Apr26 comment Calculating the highest possible damage achievable using 6 items from a pool of ~25 Probably belongs on SO. Apr25 comment Inclusion-exclusion principle: Number of integer solutions to equations @DAK: Reread Gerry's last paragraph. For the intersection of $A_1$ and $A_2$, it's equivalent to solving $v_1+v_2+y_3+y_4=5$ with $v_1, v_2, y_3, y_4 \ge 0$. Just like the number of solutions to solve $y_1+y_2+y_3+y_4 = 12$ is $C(15,3)$, the number of solutions to that equation (and the size of the $\lvert A_1 \cap A_2 \rvert$ set) is $C(8,3)$. Apr25 comment Inclusion-exclusion principle: Number of integer solutions to equations I agree, I think it's $C(12 + 4 - 1, 3) = C(15,3)$. Apr13 comment Can (x'y' + xy) be simplified? @Brandon: You should probably write that as an answer. Apr13 comment Draw customized (calculus) graphs like these? Not sure whether to flag it, but I have enough rep to retag stuff so I got rid of the graph-theory tag. Mar31 comment Interpreting “lying on the parabolas” Out of curiosity, how do you get Mathematica to make that? Mar20 comment Numbers satisfying $\binom{n}{k} = m!$ I just wrote a script and I don't believe there are any others up to 13! (except of course $\binom{n}{0}$ and $\binom{n}{1}$).