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2d
comment How to explain the concentration-of-measure phenomenon intuitively?
Dimension higher than $3$ is perplexing, that's true. Especially dimension $d \to \infty$ as in this case...
Jun
24
comment Approximation of general measurable maps by simple functions
For $Y$ a topological space, the answer is "no" in general. This is the wrong forum for the question, though.
Jun
24
comment Approximation of general measurable maps by simple functions
What is $Y$? You need some sort of convergence in $Y$ for the question even to make sense. Do you want an "order" convergence as you wrote in the real-valued case?
Jun
19
comment Bitwise operation of two square roots
So we ask about the "Nim sum" of $\sqrt{2}$ and $\sqrt{3}$: addition without carry in mod 2.
Jun
18
comment Space of continuous real-valued functions on $[0,1]^\omega$ with the weak and pointwise topology
Isomorphic as vector spaces, yes. But not as topological vector spaces. Martin is correct: the method used for $C[0,1]$ also works for this. More generally, try proving it for $C(K)$, where $K$ is an infinite compact metric space.
Jun
9
awarded  reference-request
Jun
7
comment First mean value theorem for integration and Lebesgue measureability
Non-Lebesgue measurable, no. Discontinuous, yes.
Jun
4
answered What are some examples of non-commutative $\mathbb{Q}$-monoids and/or $\mathbb{R}$-monoids?
May
31
comment Is this a rational function?
So remark 2 is even stronger than the question: this function is not algebraic
May
26
awarded  Nice Answer
May
25
comment Do non-normal states exist in the Solovay model?
And, for example, does a nonseparable Hilbert space even have an orthonormal basis ... for that I would apply Zorn's Lemma.
May
25
comment Do non-normal states exist in the Solovay model?
Are you claiming Gleason's theorem works without choice?
May
25
comment A book for problems in Functional Analysis
I looked for books at Amazon, and found that "functional analysis" is a topic in psychology, with more books than the same-name topic in mathematics...
May
25
comment Do non-normal states exist in the Solovay model?
Perhaps we need a definition or reference for: state, normal state.
May
22
answered Slightly weakened / altered concepts of a field
May
21
comment Differential Topology over $\mathbb{Q}$
For example, an uncountable disjoint union of copies of $\mathbb Q^n$. So the requirement may as well be that the whole space is countable (as Simon assumes).
May
21
comment Differential Topology over $\mathbb{Q}$
Also, we need a definition of "rational manifold". Without paracompactness you could have some sort of "long line" not of the same cardinal as the "short line" $\mathbb Q$.
May
21
comment Differential Topology over $\mathbb{Q}$
So "differentiable" means differentiable at each point of the domain? So the differential may vary from point to point? And need not depend continuously on the point?
May
20
comment Find the expansion of the exact solution (beyond Taylor)
@Carlo: He says limit $S \ll 1$ ... so you claim that is a mistake and he intends $S \to \infty$ instead?
May
20
comment Are there examples of functions in $L_1$ and $L_\infty$ whose Fourier series divergent (“weakly”)?
@user228494: Uniform boundedness principle. An interesting method to show existence. But your question asks for "some examples" and UBP is not the way to produce explicit examples.