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age 25
visits member for 3 years, 9 months
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Dec
12
comment On the problem of polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$
What this seems like is material worth a blogpost.
Dec
11
comment
Relevant
Dec
10
comment If $\sigma$ is a cycle of length $r$, then it has order $r$?
@darijgrinberg Would you like to put your comment as an answer. I'll upvote it.
Dec
10
comment
@PedroTamaroff I don't chat as often as I used to, the few times I've been there recently, I found some things that made me form some opinion. For what is worth, I remember I used to appreciate being in chat when you were around. More, when the talk was about math. Just to make clear that I'm not trying to screw you on this elections.
Dec
9
comment
The good thing about being active in chat is that many people gets to know you. This kind of behavior seems pretty much in opposite direction to lead by example and being patient and fair, not to talk about respect.
Nov
16
comment what is the set $\mathbb R[X]$ defined as?
Nice answer. Multiplication can also be defined the same way for the formal power series, so multiplication of polynomials can be realized as the restriction of that one.
Nov
12
comment If $f(x)\ge g(x)$, is $f'(x)\ge g'(x)$?
Fortunately it holds that if $f\geq g$ then $\int f\geq \int g$ with some conditions on $f$ and $g$ and several flavors of $\int$.
Nov
12
comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$
Yes, the triple equality doesn't holds in general. I misread the thing, wanted that can to be some other can't. Thank you for the clarification.
Nov
12
comment Prove $\sum_{n=1}^{\infty} n \mu(A_n) = \sum_{n=1}^{\infty}\mu(B_n) = \sum_{n=1}^{\infty} \mu(E_n)$
@DanielFischer I think you mean: "but it can't be that..." at the end of the integrals solution.
Nov
11
comment what is the cardinality of a Null set?
What kind of null set?
Nov
7
comment Is there a rationality-preserving order isomorphism between $\mathbb{Q}$ and two disjoint open intervals?
If there's an order preserving map between negative rationals (positive rationals) and rationals, one idea is to: send negative rationals to rationals to first interval, and positive rationals to rationals to second interval.
Nov
4
comment Can basis vectors have fractions?
@tokola If the vectors in the basis you found are just scalar multiples of the vectors in the solution from the book you should end up with the same diagonal matrix that they have. So maybe you made a mistake when calculating $P^{-1}AP$ or when calculating the power you mention. By the way, funny nickname.
Nov
4
comment What is the negation of the statement $f=0$ almost everywhere?
Yes, $f=0$ almost everywhere implies $f$ measurable.
Nov
4
comment What is the negation of the statement $f=0$ almost everywhere?
I pointed that because I recall that $f = 0$ almost everywhere meant the set where $f$ is not $0$ has $0$ measure. Nothing is said about the measurability of $f$. Then what I wrote.
Nov
4
comment What is the negation of the statement $f=0$ almost everywhere?
I'd say: the set $\{x:f(x)\neq 0\}$ is not measurable or there's a set $E$ with positive measure such that $f(x)\neq 0$ for each $x\in E$. This negation includes for example the characteristic function of a non measurable set. Of course what you say is fine if the function is presupposed to be measurable.
Nov
4
comment Triangle inequality
Related
Nov
1
comment On Fatou's Lemma
Limit may not always exist.
Oct
29
comment A sequence of truncates of $f$
I formatted a bit your post. Still $f_A$ isn't well defined.
Oct
29
comment How to factor $x^{4}-22x^{2}+9$ over real numbers?
This question is far more specific than what the original title suggested.
Oct
25
comment Product of bounded and convergent to $0$ sequence is a convergent to $0$ sequence
@GitGud Null sequence seems to mean sequence convergent to $0$.