Emanuele Paolini
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# 439 Comments

 Apr8 comment Riddle: 1 question to know if the number is 1, 2 or 3 Since the girl knows EVERYTHING about number 1, she knows if the boy is thinking to that number... Feb18 comment Uniform convergence and bounded increasing function. Take the functions $f_n(x) = |\sin n| x$. These are increasing functions which do not converge as $n\to \infty$. Feb7 comment Question about non conservative vector field They don't speak at all... so they are not conversative Feb3 comment Is $f(x,y)$ differentiable at the origin? What is $f'(0,a)$ when $a$ is a vector? Jan29 comment Probability of woman receiving positive mammogram and having cancer @AndréNicolas I think that the OP is exchanging the two sets in the definition of $P(A|B)$. Jan18 comment Attempt to proof the Cantor-Bernstein theorem What you write makes little sense... $f_M^{-1}(N) = M$. Maybe you mean $f_M(M)$? You should correct your question... Jan10 comment Is $0$ a natural number? @AsafKaragila I agree. Jan9 comment Is $0$ a natural number? @AsafKaragila I agree with you. But I think (please confirm) that in every country a child is taught to attach numbers to things (i.e. counting) starting from 1. I think that also mathematicians do that: Problem #1 is the first problem in the list. In my experience only computer scientists do count from zero and only when talking with computers or other computer scientists... Dec27 comment Prove that limit inferior is same as limit superior for a convergent sequence I've corrected it. I was sure my translation from italian was not good... Dec26 comment Differential geometry problem about curves I think it is the plane containing the tangent vector and the curvature vector. Dec26 comment If $f'(z_0)\neq 0$ then $f$ is one to one on some open disk $D_r(z_0)$ $\varphi(z) = g(z,z_0)$ in @Donald_Edwards answer. In fact in his answer you find $f(z)\neq f(z_0)$ and you should complete the reasoning by also varying $z_0$... which is not completely trivial. Dec13 comment Hypothetical contradiction to Bolzano-Weierstrass This works with every number, it is not required that the number is irrational. The digits can be 0... so some digit will repeat infinitely many times. Dec1 comment find the slope and intercepts of the line The same method applies to b). You need to solve for $y$. Dec1 comment How to simplify / combine function equtions containing if? There is not a unique way to simplify a function. For most purpouses the expression you have is the best way to express the function. Why you need a simplification? What's your goal? Nov30 comment Continuity of addition under the lower limit topology i've corrected it... Nov27 comment compute exponential of matrix with wolfram alpha Now I got it... MatrixExp is the right function to use. Nov25 comment Could someone explain the Lagrangian Method? the tangent to the constraint $g=0$ Nov18 comment Rolling ellipse on line - tangent and normal of roulette $F$ and $K$ are fixed on the ellipse, so their distance is fixed. At time $t$ it happens that $K(t)$ is on the line, at other times the tangent point will be different. Nov18 comment Rolling ellipse on line - tangent and normal of roulette $K$ is the center of the "infinitesimal rotation" of the point $F$. So the velocity of $F$ is perpendicular to $FK$. Nov17 comment Prove or disprove: functions Maybe $X'$ is the complementary set of $X$?