Who planted the bomb under the stage in Bodyguard?
Was it just coincidence that Tahir Mahmood went on stage?
Proof that the irrational numbers are uncountable Can someone point me to a proof that the set of irrational numbers is uncountable? I know how to show that the set $\mathbb{Q}$ of rational numbers is countable, but how would you show that the irrationals are uncountable? Re-entering the US for the third time in a year with total of 240 Days I went to the US for 90 days on an ESTA in August to November. Then back to my home country for 1 month and then back again mid December until mid February and now I am going back again after 10 days for another 90 days. Now I can see that some people refer to 180 day rule in a year. My stay will be 240 days in one year with short gaps between coming back. Is the 180 day rule accurate? Some people write that you can do unlimited trips to The US as long as you don't stay more than 90 days. Is that correct? My reason for going there the first time was to visit and travel with an American friend.  After my first visit (she is my girlfriend) moved with me to my home country but has ended up in a custody battle in the US so she needed to return urgently so I returned only to be with her and support her, not to be a tourist.  Then after my second visit I needed to go back to my sick Dad and to rent out my apartment since we left in a rush to go back to the US.  Now, my third visit is to continue to be with my girlfriend and support her in her difficult situation.   My question is, if I do end up in trouble should I tell them this whole story? Or should I just say I am visiting a friend for a third time because I want to see more of the country and I have some more time off before I go back to my job.  I have proof of money in my bank account and I stay and eat with her for free Documented proof that I have a job to return to in my home country My return ticket printed and an address to stay at in the US and I have proof I have an apartment in my home country What does **Ens** stand for? Earlier someone was asking about the category "Ens" described in Categories for the Working Mathematician. My question is more basic: What does Ens stand for?  Most of the categories have names that are self explanatory, and maybe this one does too.  But for the life of me I can't think of it, and a Google search was no help. Diffeomorphism & Weyl transformations in the 2D worldsheet of string theory and the existence of conformal gauge D. Tong's , chapter 5 (), feature the following in introducing the symmetries used in the Faddeev-Popov method:     We have two gauge symmetries: diffeomorphisms and Weyl transformations. We will schematically denote both of these by $\zeta$. The change of the metric under a general gauge transformation is $g \rightarrow g^{\zeta}$. This is shorthand for,   \begin{equation} g_{\alpha \beta} (\sigma) \rightarrow g_{\alpha \beta}^{\zeta} (\sigma)= e^{2\omega (\sigma)} \frac{\partial \sigma^{\gamma}}{\partial \sigma'^{\alpha}} \frac{\partial \sigma^{\delta}}{\partial \sigma'^{\beta}} g_{\gamma \delta} (\sigma) \end{equation}   In two dimensions these gauge symmetries allow us to put the metric into any form that we like — say, $\hat{g}$. This is called the fiducial metric and will represent our choice of gauge fixing.   Is there a proof available that shows that the combined symmetry allows us to "put the metric in any form (locally, of course)?" Is this property restricted to two dimensions? Prove that given $A\subseteq\mathbb{R}$, if has a maximum $a_0$, then $a_0$ must be the supremum.   In order to prove this, I have written the following:  Let $A\subseteq \mathbb{R}$, nonempty set because $a_{0}$ $\in A$ for hypotesis. Then, since $a_{0}$ $\in A$ is the largest element of the set $A$   (i.e. for each element $A$ of A we have that $ a\leq a_{0}$) $A$ is bounded above. Then, A has a supremum. Let $s$ be the least upper bound of $A,$ so we have that for each element $a$ of $A$, $a\leq s$, for being $s$ an upper bound. In particular, $a_0\leq s$, which implies that $s=a_0$.   Then, we have that $\sup(A)=\max(A)=a_0$, which is exactly what we wanted to prove.  Observation: this proof is true if $s \in A$   I'm not sure if my proof is correct. I will be thankful if someone tells me. Solve $p_4(x) = x^4 −(2m + 4)x^2 + (m−2)^2 $such that $p_4$ is a product of two non-constant integer-coeficient polynomials I'm having trouble getting the starting idea for a problem I've been presented with:  I need to find values for m (integer) such that the following polynomial     $p_4(x) = x^4 −(2m + 4)x^2 + (m−2)^2$; $m$ is integer   can be described as the product of two non-constant integer-coeficient polynomials.  Any help/pointers/tips on how to go about this are greatly appreciated!  Edit: I meant polynomials with integer coeficients, but for some reason typed positive. Find Nearby Accounts migration to Google Maps API v3 I have a Laars gas boiler that has 3 heating zones. I want to replace the old mercury honeywell tstat on the 1st floor (heat only) with a newer honeywell RTH9580 wifi model. I've taken pictures of my entire system, labeled the wires in the pics to indicate the associated connections, and included the Laars wiring diagram.  There is a transformer mounted on the wall near the boiler that is wired in-line to the system (power from the panel --> into the emergency boiler switch --> into the wall transformer --> then to the boiler (low water cut off and boiler circuitry).  There is also a transformer within the boiler circuitry itself.  Can someone tell me the best method (proper preferred, not necessarily easiest) to connect the C wire? Let $f$ be a nonconstant element of ring $\mathbb Z[x]$. Prove that $\langle f \rangle$ is not maximal in $\mathbb Z[x]$.   Let us assume $\langle f \rangle$ is maximal. Then $\mathbb Z[x] / \langle f \rangle$ would be a field. Let $a \in \mathbb{Z}$. Then $a + \langle f \rangle$ is a nonzero element of this field, hence a unit. Let $g + \langle f \rangle$ be its inverse. Then $a g - 1 \in \langle f \rangle$, hence $ag(x)-1 = f(x)h(x)$ for some $h \in Z[x]$, hence $ag(0) + f(0)h(0) = 1$, thus $(a,f(0))=1$ for all $a \in \Bbb Z$, contradiction, hence the proof.  Is my argument correct? Is there any other method? It's $\mathbb{Z}\subseteq \mathbb{Z}[X]/(X^5-1)$ an integral extension? It's $\mathbb{Z}\subseteq \mathbb{Z}[X]/(X^5-1)$ an integral extension?  $\mathbb{Z}[X]/(X^5-1) \simeq \mathbb{Z}[x]$ where $x^5-1=0$.  So is an integral extension because $x$ is integral  over $\mathbb{Z}$. It's right? Why is the sum of two random variables a convolution? I've been wondering about this for a while, since getting interested in knife sharpening.  When using a knife, it will get duller. One (the primary) reason being that you "bend" the edge. You fix this using a honing steel.  After a while though, you need to sharpen the knife again.  Another setting: If you have a brittle knife and/or mistreat your knife you will chip it.   As far as I can tell, this should mean that small pieces of metal (dust, shavings, etc.) come lose, and then likely get in the food.  Is this correct? Are there no health considerations when digesting small pieces of very sharp metal? Every Function in a Finite Field is a Polynomial Function How do you file a bug report for Windows? I have come across an issue that I feel is a  in Windows 7. What is the official process for submitting an issue to Microsoft from a consumers perspective as an end user of Windows? Why are downloads destructive in the Star Trek universe? There are numerous places in various Star Trek episodes where references are made to the fact that "downloads" are a destructive operation: you download something from one place, and unless you explicitly made a copy beforehand, what you downloaded is gone from its original storage location and instead appears in some other location. Hence was born the term "copy and download".  There are of course out-of-universe, plot reasons for things happening that way which are exploited from time to time. There is also the out-of-universe explanation of how large media companies feel about people downloading copyrighted works, and a possible out-of-universe explanation that at the time, people in general may not have been intimitely familiar with the implications of the term "download", so they added "copy" to help describe what happens to at least portions of their viewership.  But is there a plausible in-universe explanation for why downloads would be destructive by default, and a specific copying operation would have to be made beforehand so as to not delete the data from its original location?  As for specific examples, these are two that I can think of right now (I'm quite sure there are more):   VOY "Twisted" (S2E06), right near the end, stated by Torres: "Our entire database has been copied and downloaded into somebody else's system." VOY "Message In A Bottle" (S4E14), a little more than five minutes into the episode, the EMH is "downloaded into the transceiver array" for transmission across an alien sensor network to the Prometheus when the latter is in the alpha quadrant, and some 20 minutes into the episode it's established that the EMH is not available in the sickbay and will return later. Motivation behind the definition of ideal class group Why does Sass change the format of my colors? Bibliography per chapter with continuous numbering I would like to create a document with two chapters. After the first chapter there should be a bibliography. The next chapter should be able to reference items of the former chapter, but only show the new items in its bibliography, starting with the next number from the first bibliography.  Example:     Chapter 1 - The Fu   Fu has been done by Bar [1]. Early versions ...   Bibliography   [1] Bar et. al., Doning the Fu      Chapter 2 - Compining Fu with Herp   Doning Fu as described in [1]   neglects the advantages of Herp pointed out by Derp [2].   Consequently ....   Bibliography   [2] Derp et. al., The Advantages of Using Herp   Please not too much discussion about if that is a friendly-to-use idea, it is not my own demand :) Uniformly Continuous Function sending Bounded Set to Unbounded One Let $(X,d)$ and $(Y,\rho)$ be metric spaces, and let $f: X \to Y$ be a uniformly continuous function. If $A \subset X$ is bounded, must $f(A) \subset Y$ be bounded?  It is clear to me that in metric spaces that satisfy the Heine-Borel property, such as $\mathbb{R}^{n}$, the answer to this question is yes. However, I can see no reason why this should hold for arbitrary metric spaces. Any ideas? Thanks! Why does the speed of light in vacuum have no uncertainty? I could understand that the definition of a second wouldn't have an uncertainty when related to the transition of the Cs atom, so it doesn't have an error because it's an absolute reference and we measure other stuff using the physical definition of a second, like atomic clocks do.  But why doesn't the speed of light have uncertainty? Isn't the speed of light something that's measured physically?  Check out that .