Is there a Lebesgue measurable subset $A \subset R$ such that for every interval $(a,b)$ we have $0 < \lambda(A\cap(a,b))< (b-a)$
How to get a set $E$ such that $0<\mu(E\cap I)<\mu(E)$ for all interval $I$?
The determinant of block triangular matrix as product of determinants of diagonal blocks I am given the following partitioned, upper-triangular matrix:  $$ \begin{bmatrix}   A_1 &amp;*  &amp;*  &amp;*  &amp;*  &amp;*  \\    0&amp; A_2 &amp;*  &amp;*  &amp;*  &amp;*  \\    .&amp;  0&amp; A_3 &amp;*  &amp;*  &amp;*  \\    .&amp;  0&amp;  0 &amp;...  &amp;*  &amp;. \\    .&amp;  0&amp;  0&amp;  0&amp; ... &amp;.  \\    0&amp;  .&amp;  ...&amp;  0&amp;0 &amp; A_m \end{bmatrix} $$  where each of the $A_i$ are block-matrices.  I have to prove that the determinant of this general matrix is: $$ \prod_{n=1}^m \det A_i. $$  We already proved in class that it is true for $ m=2 $ and we can use it in our proof.  Thanks for your answers! Is temperature in vacuum zero? From      The temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms.    Now if I remove all the particles from the box shown below will the temperature be zero? Why 32bits OSs can't address more than 3.2/3.2 gb of memory? Don't know if this is the right place to ask this question.  I've been reading that 32bit OSs (like the Ubuntu i'm running right now) can't adress more than 3.2gb or 3.3gb of RAM memory.  I remember for my old Computer Architecture course that the memory limitation was 2^32 "pointers" (don't remember the right word). I mean, the memory was represented like an array where the CPU can acces it directly, but up to its limit. If the CPU is 32 bit, then it can address 2^32 words, if it's 64 bits 2^64, etc.  So, if what i said before is right, then, my OS should be able to address 2^32 = 4294967296 = 4Gb.  I'm thinking maybe some sort of space is reserved to the particular use of the Kernel, cache, buffering or swapping. But don't have the correct answer.  Can you give me a hint? PostgreSQL multi-column unique constraint and NULL values I have a table like the following:  create table my_table (     id   int8 not null,     id_A int8 not null,     id_B int8 not null,     id_C int8 null,     constraint pk_my_table primary key (id),     constraint u_constrainte unique (id_A, id_B, id_C) );   And I want (id_A, id_B, id_C) to be distinct in any situation. So the following two inserts must result in an error:  INSERT INTO my_table VALUES (1, 1, 2, NULL); INSERT INTO my_table VALUES (2, 1, 2, NULL);   But it doesn't behave as expected because according to the documentation, two NULL values are not compared to each other, so both inserts pass without error.  How can I guarantee my unique constraint even if id_C can be NULL in this case? Actually, the real question is: can I guarantee this kind of uniqueness in "pure sql" or do I have to implement it on a higher level (java in my case)? apt-get update fails to fetch files, “Temporary failure resolving …” error Oxford Comma Conventions According to the Wikipedia page for the , "Use of the comma is consistent with conventional practice" and "Use of the comma is inconsistent with conventional practice." Did the Oxford Comma come before its omission, or was the Oxford Comma traditionally omitted?  It makes logical sense that every item in a list would be separated in the same way: by a comma. If the Oxford Comma is conventionally correct, when and why did people begin to omit it? Issues Doing a String Comparison in LINQ Define functions in structs How does Duff's device work? It's using Euclidian inverse. Can you show it step by step?   $$N=7, q=11, a = 3+2X^2 -3X^4 +X^6$$  the inverse of $a \pmod {11}$ is  $$A=-2+4X+2X^2 +4X^3 -4X^4 +2X^5 -2X^6$$  How do we compute $A$? Symmetric Inequality in $\mathbb{R}$ Is it possible to run an x86 binary on an ARM processor? How to convert numbers between hexadecimal and decimal Can I register a domain name that contains a company name or trademark? I wonder is it legal to register a domain name that contains a company name. For example cococola.cc (considering that this domain name is available). Can I buy and use any domain names that contain a name of a trademark? I have a residence permit (permesso di soggiorno) for Italy. I am currently in the Netherlands for an exchange. My permit expired on the 30th of November and I applied for a new one but I will get the card in January. I have the documents supporting that I have applied for the renewal of the permit. In the middle I want to travel to Italy for Christmas and come back to the Netherlands.    Would this be a problem? How do Southern people discern Night's Watch deserters from truthful brothers sent south? Night's Watch deserters are sentenced to death, as we've seen in the very first episode of Game of Thrones. A man dressed all in black is apprehended by Stark men and brought before Lord Eddard Stark. Lord Stark sees him as a deserter and sentences him to die (and then executes that death penalty).  However, there are men of the Night's Watch south of the Wall, on a legitimate mission or on some kind of allowed leave. For instance, we have Benjen Stark visiting Winterfell when the king and his party is there. There is also Yoren, who travels around Westeros in search of new recruits.  I could imagine that the Warden of the North (and other lords in the northern part of Westeros) would have a good idea of who would be allowed further south and whose appearance would raise suspicion. But I reckon the southern lords don't have as many visits from the Night's Watch, so they might not know who would be allowed to be there and who wouldn't.  How would lords who are rather unfamiliar with the specific brothers of the Night's Watch discern deserters from brothers sent out for some reason?  That ends my question, but there is a spoiler from the season 5 finale that continues the question a bit more:      Sam is sent to Oldtown to become a Maester, so he can replace Maester Aemon at Castle Black.  But he is riding together with Gilly (a woman!) and her baby (a baby!), which might raise a lot of suspicion from people who don't know what he is sent out to do.  What prevents southern lords of sentencing Sam as a deserter from the Night's Watch? How can I read off the fact that gravity is associated with spin-2 particles from the Einstein-Hilbert action? I have often heard that the gravitational field has spin $2$. How can I read the spin of the field from the Einstein-Hilbert action  $$S=\int \! \mathrm{d}^4x \,\sqrt{|g|} \, \mathcal{R} \, \, \, ?$$ How do I stop Windows 10 from updating my graphics driver? Every time Windows 10 runs updates (which I see no way to control), it updates my graphics driver.  I like the old one because it is faster.  So, I have to reinstall it.  This is getting to be a pain.  Is there any way to stop Windows 10 from updating it again? $$Rad(I)=\{a \in R | \exists n \in \mathbb{N} \text{ such that } a^n \in I\}$$   R is a commutative ring, I is an ideal.   To show that $Rad(I)$ is an ideal of $I$, we have to show that for $a,b \in Rad(I)$ it stands that $a-b \in Rad(I)$ and for $r\in R$ it stands that $a\cdot r\in Rad(I)$, right??   When $a,b \in Rad(I)$ we have that $a,b \in R$ and $a^n, b^m \in I$.   $a-b \in R$.   But how can we show that $(a-b)^x \in I, x \in \mathbb{N}$ ?? Rules and guidelines for drawing good schematics There are a lot of poorly drawn schematics here. A few times people have actually asked for critiques of their schematics. This question is intended as a single repository on schematic drawing rules and guidelines can point people to. The question is  What are the rules and guidelines for drawing good schematics?     Note: This is about schematics themselves, not about the circuits they represent.