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University of Florence


2d
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 $P(A|B)$.
Jan
18
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...
Jan
10
comment Is $0$ a natural number?
@AsafKaragila I agree.
Jan
9
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...
Dec
27
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...
Dec
26
comment Differential geometry problem about curves
I think it is the plane containing the tangent vector and the curvature vector.
Dec
26
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.
Dec
13
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.
Dec
1
comment find the slope and intercepts of the line
The same method applies to b). You need to solve for $y$.
Dec
1
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?
Nov
30
comment Continuity of addition map with lower limit topology
i've corrected it...
Nov
27
comment compute exponential of matrix with wolfram alpha
Now I got it... MatrixExp is the right function to use.
Nov
25
comment Could someone explain the Lagrangian Method?
the tangent to the constraint $g=0$
Nov
18
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.
Nov
18
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 $FK$.
Nov
17
comment Prove or disprove: functions
Maybe $X'$ is the complementary set of $X$?
Nov
11
comment Limit of derivatives and continuous
$\lim_{x\to 1^-} f'(x) = \lim_{x\to 1^-} \frac{1}{(1-x)^2} = +\infty$, it exists even if it is not finite.
Nov
7
comment Limit of derivatives and continuous
But, again, this is true only if the limit of $f'$ exists and it is finite.
Nov
7
comment Limit of derivatives and continuous
It is possible that the limit of $f$ is infinite and the limit of $f'$ exists. Take $f(x) = 1/(1-x)$.
Nov
7
comment Limit of derivatives and continuous
It is correct if you take $h(x) = g(1/2) + \int_{1/2}^x g'(t)dt$ (check the sign).