Henning Makholm
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 22h comment Probabilities of Unique Numbers in Roulette How many zeroes does your roulette wheel have? 1d revised Prove that if $\gcd (a,n)=1$, $as=1 \pmod n$ has a solution edited tags 1d comment for $I = [0,1]$, is $I\times I$ convex in $\mathbb{R} \times \mathbb{R}$? Your definition of "convex" works only for $\mathbb R^1$. You should have one for general vector spaces that does not depend on having an ordering -- something like for all $a,b\in Y$ and every $t\in[0,1]$ it holds that $ta+(1-t)b\in Y$ too. 1d comment Prove that multiplication is well defined It is probably easiest to prove it in two steps: First, if $(a,b)\sim(a',b')$ then $(a,b)(c,d)\sim(a',b')(c,d)$. Then the same thing to the other side: if $(c,d)\sim(c',d')$ then $(a',b')(c,d)\sim(a',b')(c',d')$. Splitting it up like this will allow you to attack each part with the distributive law. 1d comment How can I express the NOT in terms of AND, XOR, XNOR Actually NOR alone is a known complete set ... 1d comment Having trouble interpreting the geometry of this setup. Your drawing looks right to me. The problem says that the cross-section of the conductor has metal in the region between the two circles and nothing (air or some other dielectric) within the small circle. 1d comment Peano Arithmetic and Riemann Hypothesis. @User1: Yes -- PA proves every true $\Delta_0$ sentence, so it disproves every false $\Delta_0$ sentence, so a counterexample to a $\Pi_1$ sentence is immediately a disproof. 1d comment Peano Arithmetic and Riemann Hypothesis. @User1: There are several possibilities -- I had Robin's one in mind, but that's good too. 1d comment Peano Arithmetic and Riemann Hypothesis. One also needs to know that the Riemann Hypothesis is known to be equivalent to a $\Pi_1$ sentence in the language of arithmetic. It is that equivalent sentence that would be "provable (or not) in PA". Due to the property Asaf mentioned, every $\Pi_1$ sentence that is consistent with PA (i.e. not disprovable by PA) is true in the standard integer. Feb 6 comment Given a normal $A_{n\times n}$ matrix, then $\lVert A^*v \rVert = \lVert Av\rVert$ and $\langle Av,v\rangle = \langle A^*v,v\rangle$ (1) Even for real numbers $k$ and $r$, it is possible to have $|k|=|r|$ without $k=r$. When $k$ and $r$ can be complex there are even more ways to do this. And we always have $|z|=|\bar z|$ even when $z$ is not real. Feb 6 answered What is the general term of the sequence $u_{n+1}=c u_n+d$? Feb 5 comment Finding disc of convergence @lisyarus: Because I'm overcomplicating it. Of course that is better. Feb 5 revised Finding disc of convergence deleted 1 character in body Feb 5 answered Finding disc of convergence Feb 4 comment Expansion of $\cos \sqrt x$? @Hagen: It's a valid expansion of the unique analytic continuation of $\cos\sqrt x$, though. Feb 4 comment Expansion of $\cos \sqrt x$? Try the substitution! Since the series for $\cos \theta$ only uses even powers of $\theta$, all the problematic terms vanish! You know the resulting series converges for $x>0$, and it certainly converges for $x=0$, so its radius of convergence is infinite, and you get an analytic continuation to negative reals (and arbitrary complex numbers) for free! Feb 3 comment Reasoning ( CSIR NET December 2015) That is well and good, though sexual orientation doesn't really come into it as long as the son has exactly one father. The greater problem is how the questioner imagines relations to be classified into "types" here. It appears that "a polygamous family" counts as a "type of relation", and the statement can certainly be true there (one man, at least two women, speaker is one of the women) -- but it can also be true in a traditional nuclear family, so based on that it is hard to escape (3) being the right answer rather than (2). Feb 3 revised Is $(-\infty, 0)$ the same size as $(0, \infty)$? edited tags; edited tags Feb 3 comment Subsets of the reals when the Continuum Hypothesis is assumed false It can't be open either. Feb 3 awarded elementary-number-theory