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University of Florence


Oct
9
comment If $f$ is an increasing function defined on $[a,b]$ . Then, $f$ has countable number of discontinuities
Points of continuity must only be searched into the domain of the function, since the definition of continuity requires the value of the function to be computed in the point. If you decide that a function is not continuous where it is not defined, then the function $f(x) = \sqrt(x)$ would be discontinuous for every $x<0$ which is a not-countable set.
Oct
1
comment About Banach Spaces And Absolute Convergence Of Seires
Choose $n_k$ so that $|x_m - x_{n_k}|<2^{-k}$ for all $m>n_k$. This is possible by the definition of Cauchy sequence.
Sep
30
awarded  Explainer
Sep
29
revised Choosing two random numbers in $(0,1)$ what is the probability that sum of them is more than $1$?
[Edit removed during grace period]
Sep
24
awarded  Autobiographer
Sep
21
revised How to find $F(x) = \int_x^{x^2} (2+\sqrt t )\, dt$ ?
deleted 36 characters in body
Sep
21
comment How to find $F(x) = \int_x^{x^2} (2+\sqrt t )\, dt$ ?
Write the intermediate passages
Sep
15
comment existence of a differentiable function under certain given condition
The requirements on $f(0)$ and $f'(0)$ don't mean anything. Maybe it was $x=0$?
Sep
15
comment Constructing a circle from a square
The example you found is exactly a proof that perimeter is not continuous. And when I speak of "metric" I mean a distance between sets, not points. There is no such a think like Euclidean metric on the family of sets. Look for example at en.wikipedia.org/wiki/Hausdorff_distance
Sep
15
revised Constructing a circle from a square
added 310 characters in body
Sep
15
answered Constructing a circle from a square
Sep
15
comment Ellipsoidal Decomposition: Finding ellipsoids whose sum contains a given ellipsoid
You mean: the union of these two ellipsoids encloses $E$? But the union of them will not be an ellipsoid...
Sep
12
reviewed Approve suggested edit on Order of error of a fraction
Aug
27
answered How to graph functions without a calculator?
Aug
27
revised Verify my proof: If $X$ is infinite, then there exists $f: \mathbb{N} \rightarrow X$ such that $f$ is injective.
deleted 3 characters in body
Aug
27
comment Verify my proof: If $X$ is infinite, then there exists $f: \mathbb{N} \rightarrow X$ such that $f$ is injective.
@Guilherm: I cannot understand your proof. Seems you are saying: take the function $f$ such that the maximal set where $f$ is injective, is maximal. It's not clear at all how you can define such things. Take $f(n)=\lfloor n/2\rfloor$ and explain what is $k$ for such a function. Also the notation $a \neq b \neq c$ is bad, don't use it.
Aug
26
answered Verify my proof: If $X$ is infinite, then there exists $f: \mathbb{N} \rightarrow X$ such that $f$ is injective.
Aug
26
answered Is the dot product valid for coordinate vectors of infinite length?
Aug
26
revised Can I conjugate a complex number: $\sqrt{a+ib}$?
added 50 characters in body
Aug
26
answered Can I conjugate a complex number: $\sqrt{a+ib}$?