User alberto.bosia - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T01:34:25Z http://mathoverflow.net/feeds/user/20692 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/86948/measure-theory-and-continuum-hypothesis measure theory and continuum hypothesis alberto.bosia 2012-01-29T08:53:24Z 2013-02-21T18:37:47Z <p>let's assume $\neg CH$, then there's a set $X$ such that $|\mathbb N|&lt;|X|&lt;|\mathbb R|$. i'm wondering about the lebesgue measure of such set... is it even possible to measure it? would it be possible that its measure is more than $0$? i think not, because all the subset of cantor set are measure $0$ sets, and there would be a set $K$ such that $|X|=|K|$ and $K\subset Cantor$. is it correct?</p> http://mathoverflow.net/questions/28612/do-names-given-to-math-concepts-have-a-role-in-common-mistakes-by-students/89685#89685 Answer by alberto.bosia for Do names given to math concepts have a role in common mistakes by students? alberto.bosia 2012-02-27T17:53:51Z 2012-02-27T17:53:51Z <p>In italian, the words <em>bound</em> and <em>limit</em> sound the same, "limite". This often causes confusion, like in the <em>limit points</em> and the <em>boundary points</em> of a set or a <em>bounded function</em> and its <em>limit</em>.</p> http://mathoverflow.net/questions/88284/how-to-get-rich-in-a-hilberts-hotel/89633#89633 Answer by alberto.bosia for How to get rich in a Hilberts Hotel? alberto.bosia 2012-02-27T04:22:23Z 2012-02-27T04:22:23Z <p>If the distance matters, one could ask his neighbors what's the distance between them and their neighbors, to understand what the actual position of $e$ is; then is possible to send money as you pointed out.<br> Well, this is probably cheating on the definition of "unlabeled" copies...</p> http://mathoverflow.net/questions/88875/antiderivative-of-a-darboux-function antiderivative of a darboux function alberto.bosia 2012-02-19T01:09:23Z 2012-02-22T00:58:55Z <p>this is probably a very common question, but i couldn't find the answer on my books.<br> is every darboux function the derivative of a function? even the nowhere continuous ones?</p> http://mathoverflow.net/questions/88871/why-is-this-rational/88872#88872 Answer by alberto.bosia for Why is this rational? alberto.bosia 2012-02-19T00:44:36Z 2012-02-19T00:44:36Z <p>It is not known if it is rational. It's suspected to be transcendental over $\mathbb Q$. It is known that $e^\pi$ is transcendental, but none of $e^e,\pi^e,\pi^\pi$ is known to be irrational or transcendental.</p> http://mathoverflow.net/questions/86795/surjective-function-from-non-measurable-sets surjective function from non-measurable sets alberto.bosia 2012-01-27T06:17:24Z 2012-02-01T11:14:37Z <p>let $V$ be the vitali set and let $g:V\to\mathbb R$ be a surjective function. then the fuction $f:\mathbb R\to\mathbb R$ such that $f(x)=g([x])$ will be a function that is surjective in any interval of the real line. i know the examples with base 9 digits, but this one would be much easier.</p> <p>is there a "standard" way to construct surjective and bijective functions from non-measurable sets to measurable ones with the same cardinality?</p> http://mathoverflow.net/questions/86769/conjecture-of-normal-algebraic-numbers conjecture of normal algebraic numbers alberto.bosia 2012-01-27T00:04:37Z 2012-01-27T03:57:47Z <p>what has led to conjecture that all the irrational algebraic numbers are normal? is there some kind of evidence somewhere?</p> <p>i know that there exists non-normal trascendental numbers like liouville's number. is this the only thing that "started" the conjecture?</p> http://mathoverflow.net/questions/86360/continuation-of-the-n-th-derivative-function continuation of the "n-th derivative" function alberto.bosia 2012-01-22T09:09:48Z 2012-01-22T09:19:24Z <p>let $D_{\mathbb N}$ be the standard "n-th derivative" function</p> <p>is it possible to make a continuation of $D_{\mathbb N}$ to non integer values?</p> <p>i mean a function $D_{\mathbb R}$ such that $D_{\mathbb R}(x,f)=D_{\mathbb N}(n,f)$ for all $x=n\in\mathbb N$</p> <p>it should be something relevant, linear interpolation usually doesn't make any sense.</p> http://mathoverflow.net/questions/86049/is-there-a-periodic-function-without-minimum-period-such-that-all-the-possible-pe Is there a periodic function without minimum period such that all the possible periods are irrationals? alberto.bosia 2012-01-19T00:24:23Z 2012-01-19T01:40:32Z <p>Let $f:\mathbb R\to\mathbb R$ be a periodic function. We say $f$ is without minimum period if, $\forall t$ such that $f(x+t)=f(x)\forall x$, there is a $t'$ such that $0 <p>Is there a periodic function without minimum period such that$P_f\cap\mathbb Q=\emptyset$?</p> http://mathoverflow.net/questions/86049/is-there-a-periodic-function-without-minimum-period-such-that-all-the-possible-pe/86050#86050 Answer by alberto.bosia for Is there a periodic function without minimum period such that all the possible periods are irrationals? alberto.bosia 2012-01-19T00:25:54Z 2012-01-19T00:44:24Z <p>this is the complete question, sorry.</p> <p>Let$f:\mathbb R\to\mathbb R$be a periodic function. We say$f$is without minimum period if,$\forall t$such that$f(x+t)=f(x)\forall x$, there is a$t'$such that$0 &lt; t' &lt; t$and$f(x+t')=f(x)\forall x$.</p> <p>The easiest examples of such functions are constant functions.</p> <p>Dirichlet's function ($1$if$x\in\mathbb Q$and$0$if$x\not\in\mathbb Q$) too is a periodic function without minimum period, cause$\forall q\in\mathbb Q$it's true that$f(x+q)=f(x)$.</p> <p>Let's say that$P_f$is the set of all possible periods of$f$. (example:$P_{constant}=\mathbb R$,$P_{dirichlet's}=\mathbb Q$)</p> <p>Is there a periodic function without minimum period such that$P_f\cap\mathbb Q=\emptyset$?</p> http://mathoverflow.net/questions/85954/how-do-you-know-something-have-to-published How do you know something have to published? alberto.bosia 2012-01-18T04:10:59Z 2012-01-18T04:10:59Z <p>how do you know your work is worthy to be published?</p> <p>i mean: you start studying a non-trivial topic. at the beginning you don't get much results, cause you still don't have a full understanding of what your topic really relies on. then suddenly you get it. and it simple, so very simple that any undergradate may understand it, but it's not a commonly known result.</p> <p>do you just send your paper to a famous journal (and hope they don't reject it)?</p> http://mathoverflow.net/questions/90492/power-of-two-plus-integer-is-not-prime Comment by alberto.bosia alberto.bosia 2012-03-09T00:27:17Z 2012-03-09T00:27:17Z has anybody noticed that$k$is even infinitely many times? http://mathoverflow.net/questions/89861/zeros-of-riemann-zeta-function Comment by alberto.bosia alberto.bosia 2012-02-29T13:07:59Z 2012-02-29T13:07:59Z wouldn't one have to use a complex analysis book? http://mathoverflow.net/questions/89811/set-up-latex-margin Comment by alberto.bosia alberto.bosia 2012-02-28T23:47:08Z 2012-02-28T23:47:08Z @Juan: that's such a great answer! http://mathoverflow.net/questions/87437/die-rolling-hamiltonian-cycles/89493#89493 Comment by alberto.bosia alberto.bosia 2012-02-27T04:02:32Z 2012-02-27T04:02:32Z this is really an amazing answer http://mathoverflow.net/questions/89057/interesting-level-curves Comment by alberto.bosia alberto.bosia 2012-02-21T00:24:13Z 2012-02-21T00:24:13Z you should probably retag this as a soft question http://mathoverflow.net/questions/88997/two-shapes-in-a-2n-times-2n-grid-sheet-can-we-pick-third-one Comment by alberto.bosia alberto.bosia 2012-02-20T22:29:56Z 2012-02-20T22:29:56Z can you show it? i can't figure it out... i'm not good in such problems. http://mathoverflow.net/questions/88997/two-shapes-in-a-2n-times-2n-grid-sheet-can-we-pick-third-one Comment by alberto.bosia alberto.bosia 2012-02-20T08:02:56Z 2012-02-20T08:02:56Z why not four copies? http://mathoverflow.net/questions/88914/a-formula-for-pin Comment by alberto.bosia alberto.bosia 2012-02-19T12:17:03Z 2012-02-19T12:17:03Z that's ENORMOUSLY off topic, and i'm pretty sure you didn't find an analytic formula for$\pi(n)$. http://mathoverflow.net/questions/88930/online-free-copy-of-the-article-what-is-an-answer-amer-math-monthly Comment by alberto.bosia alberto.bosia 2012-02-19T12:12:00Z 2012-02-19T12:12:00Z there's a big .torrent archive of the Monthly, available for free online. well, it's probably illegal... http://mathoverflow.net/questions/88875/antiderivative-of-a-darboux-function/88887#88887 Comment by alberto.bosia alberto.bosia 2012-02-19T12:08:47Z 2012-02-19T12:08:47Z thanks, that's what i feared. i'll get the <i>Bruckner</i> asap. i think it's necessary to assume that the function is at least$L^1$. http://mathoverflow.net/questions/87386/counting-patterns-in-a-word Comment by alberto.bosia alberto.bosia 2012-02-03T00:46:05Z 2012-02-03T00:46:05Z there will probably never be an algorithm that finds ALL the patterns in a word, it's too general. of course you can code a program to find a lot of specific patterns, like increasing sequences, but first of all, you should define what you call &quot;pattern&quot;: is &quot;246&quot; a pattern? &quot;963&quot;? http://mathoverflow.net/questions/86795/surjective-function-from-non-measurable-sets Comment by alberto.bosia alberto.bosia 2012-01-27T19:15:16Z 2012-01-27T19:15:16Z take the equivalence relation$x\sim y\Leftrightarrow x-y\in\mathbb Q$, then take the quotient set$R/\sim$. this is basically the vitali set.$[x]$is the class of$x\$ in the quotient. http://mathoverflow.net/questions/86405/a-9-pages-integral Comment by alberto.bosia alberto.bosia 2012-01-22T21:53:17Z 2012-01-22T21:53:17Z why does mathematica produce such result? i can't even read it http://mathoverflow.net/questions/86405/a-9-pages-integral Comment by alberto.bosia alberto.bosia 2012-01-22T21:52:09Z 2012-01-22T21:52:09Z indefinite integral http://mathoverflow.net/questions/86360/continuation-of-the-n-th-derivative-function/86362#86362 Comment by alberto.bosia alberto.bosia 2012-01-22T09:22:53Z 2012-01-22T09:22:53Z that's exactly what i was thinking about! i never knew such thing existed. thanks a lot