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University of Florence


Jun
25
answered What is the domain of the function $F(x)=\int_{0}^{x}\frac{\operatorname{arctan}(t)}{t}dt$?
Jun
12
comment probability in roulette!
The best thing you can is not to play.
Jun
11
comment Solve set problems without Venn diagrams
@MauroALLEGRANZA my position is that your solution is using the inclusion-exclusion principle when you say: in order to avoid counting twice. Once you assume that the equation given by this principle is true, then the problem becomes algebraic. Notice that this principle is about finite sets and can be understood without knowning anything about general set theory (let alone Cantor).
Jun
11
answered Find all the asymptote of $1-x+\sqrt{2+2x+x^2}$
Jun
11
answered $l_{p}$ metric on $\mathbb{R}^{n}$ and its open balls
Jun
11
comment $l_{p}$ metric on $\mathbb{R}^{n}$ and its open balls
1. cannot read indices in the answer. 2. what you mean with ??
Jun
11
comment Solve set problems without Venn diagrams
@AsafKaragila I don't know category theory. However you could explain your position by solving the stated problem using combinatorics without set theory.
Jun
11
answered Is there a parametric form for a degenerate conic section?
Jun
11
comment Solve set problems without Venn diagrams
@AsafKaragila I would say that combinatorics is based on set theory... I cannot imagine an axiomatization of combinatorics which does not use sets. Instead I can imagine an axiomatization of numbers (real or natural) without sets.
Jun
11
revised Solve set problems without Venn diagrams
added 371 characters in body
Jun
11
comment Solve set problems without Venn diagrams
I would say no: because the statement of the problem itself can only be modeled by using sets. A purely algebraic solution cannot explain why the formula used is true.
Jun
11
answered Solve set problems without Venn diagrams
Jun
11
comment How to find the number of possible permutations in a composition function
You found $khk = h^3$. Multiply both sides of equation by $k$ on the right to obtain: $khkk = h^3 k$. But you know that $kk=1$ hence you obtain $kh = h^3 k$. About $kh^3 = kh$ you can multiply on the left by $k$ and obtain $h^3 = h$ which becomes $h^2=1$ which is false.
Jun
11
answered Differentiability of $f(x) = x \sin \frac{1}{x}$ for $x \neq 0$ and $0$ for $x = 0$.
Jun
11
comment How to find the number of possible permutations in a composition function
I don't use any theorem, just some algebraic computation. What is not clear?
Jun
11
revised How to find the number of possible permutations in a composition function
added 444 characters in body
Jun
11
answered How to find the number of possible permutations in a composition function
Jun
2
awarded  Revival
May
30
comment Is $e^{i\pi}+1=0$ all it's cracked up to be?
$e^{i\tau} = 1$
May
30
comment Prove $ \int_{C}fdr=\int_{S}dS\times\nabla f$
$f$ is a scalar function? The integral on the left seems to be a scalar value while the one on the right seems to be a vector...