So it's my understanding that the current models predict that a super massive object will collapse beyond the event horizon into a singularity of infinite density.  My question is the following: isn't such a prediction contradicted by the observable universe, since we observe expansion from the Big Bang? How could a singularity form if at some point in time there was a much more massive and dense object (the Universe) that did not remain or achieved singularity but inflated ?  edit 1: Or in other words, as Tom B. suggested [but see edit 2]:      IF the universe was inside of its own event horizon, which seems   reasonable given its huge mass and tiny size just after the big bang,   how did it escape?   edit 2 [edited a bit the initial question, comments below]: I believe this question is different from  question, because I'm not suggesting that the forces leading to black hole formation would counteract the Big Bang.   I'm indicating that there are two potential instances  of singularity in the Universe, the Big Bang t0, and black-hole singularities. The Big Bang singularity (if it ever existed) is not stable and can be observed to have degraded into inflation.  Similarly, shouldn't this observation lead one to think that a black-hole singularity, if formed, would lead to a similar inflation? I understand that the black-hole environment is not homogenous whereas the big-bang conditions were mostly homogenous, but from both singularities' referentials would that matter?
Wasn't the density of the universe at the moment after the Big Bang so great as to create a black hole? If the answer is that the universe/space-time can expand anyway what does it imply about what our universe looks like from the outside?
I need to process a large file, around 400K lines and 200 M. But sometimes I have to process from bottom up. How can I use iterator (yield return) here? Basically I don't like to load everything in memory. I know it is more efficient to use iterator in .NET. cardinality of all real sequences I was wondering what the cardinality of the set of all real sequences is. A random search through this site says that it is equal to the cardinality of the real numbers. This is very surprising to me, since the cardinality of all rational sequences is the same as the cardinality of reals, and it seemed fairly intuitive to me that if cardinality of a set $A$ is strictly greater than the cardinality of the set $B$, then cardinality of $A^{\mathbb{N}}$ should be strictly greater than cardinality of $B^{\mathbb{N}}$. It turns out to be false.  Some technical answers have appeared in this forum elsewhere but I do not understand them. As I am not an expert in this topic, could some one explain me in simple terms why this is happening?  Also is the cardinality of all functions from reals to reals also the same as the cardinality of reals? Coauthoring with a reviewer possible? I recently submitted an article to a math journal and got a response from a reviewer, with an attachment. In it, I have found some good  advice that could improve my article tremendously.  I am a bit suspicious of its accuracy since it could resolve what I have been working with for some months in a few  sentences.   But anyway, it was enough for me to ask the reviewer for coauthoring with me.   My question would be, does it often happen that an author asks a referee for coauthoring during the review process? Or could it even be possible?  I was given a month to revise my article, but the chance that I could revise successfully by myself seems to be fat.  I would be looking forward to any advice.  Thanks in advance. Is this noun used as an adjective? I read this recently in :     At the end of the summit, the French and European officials had   claimed a points victory over the Germans by getting them to agree   more firmly to a target date of January 1st next year to entrust the   European Central Bank (ECB) with the ultimate authority to supervise   the euro zone’s 6,000-odd banks.   "Points" is a plural, and I suppose it doesn't function as a noun in this sentence since it's following the article "a", so is it an adjective adorning "victory"? How would you count occurrences of a string (actually a char) within a string? I am doing something where I realised I wanted to count how many /s I could find in a string, and then it struck me, that there were several ways to do it, but couldn't decide on what the best (or easiest) was.  At the moment I'm going with something like:  string source = "/once/upon/a/time/"; int count = source.Length - source.Replace("/", "").Length;   But I don't like it at all, any takers?  I don't really want to dig out RegEx for this, do I?  I know my string is going to have the term I'm searching for, so you can assume that...  Of course for strings where length > 1,  string haystack = "/once/upon/a/time"; string needle = "/"; int needleCount = ( haystack.Length - haystack.Replace(needle,"").Length ) / needle.Length; Story identification - "bless the beasts that bless us" I'm trying to trace what was probably a short story rather than a full novel from my childhood.  I think it starts in the present day (so the 80s or thereabouts) and there was some kind of alternate reality bleed which meant there were (i think) ghost boars or pigs, they were becoming more physical with time, and so problematic. The family escaped when the family dog led them to and through a portal which they couldn't perceive to a safer place.  In the end, they ended up in some kind of rural community who had a religion / custom that required them to say "Bless the beasts that bless us" but some folk shortened it to BTBTBU which irritated the girl who was the principle character.  I used to read a lot of kids short story sci-fi and fantasy including Nicolas Fisk but I don't know whether this was from a compilation of several authors or a single author's collection. consider the following subsets of complex plane $$\Omega_1=\left\{c\in\Bbb C:\begin{bmatrix}1&amp;c\\\bar c&amp;1\\ \end{bmatrix}\text{ is non-negative definite } \right\} $$  $$\Omega_2= \left\{c\in\Bbb C:         \begin{bmatrix}         1 &amp; c &amp; c \\         \bar c &amp; 1 &amp; c \\         \bar c &amp; \bar c &amp; 1 \\         \end{bmatrix} \text{ is non-negative definite } \right\}$$  Let $$\bar D=\{z\in\Bbb C:|z|\le1\}$$ Then 1) $\Omega_1=\bar D,\Omega_2=\bar D$  2). $\Omega_1\neq\bar D, \Omega_2=\bar D$  3). $\Omega_1=\bar D, \Omega_2\neq\bar D$  4). $\Omega_1\neq\bar D, \Omega_2\neq\bar D$  How to proceed? Thank you. It would be nice to update the profile page from within the app.  Perhaps not many people update their profiles more frequently, but when required to do so, I would prefer to do it from the app instead of the mobile browser. Environment.TickCount vs DateTime.Now I try to understand and visualize myself covariance matrix. Supposing I have a matrix A = [ 2 3 4; 5 5 6 ], how do I calculate its covariance matrix, and what is its practical meaning? (All I was able to understand by now is that on the diagonal of the covariance matrix, variances for particular variables are placed, and on the upper and lower fields correlations between those variables.) Prove : $p$(n│even number of ODD parts)=$p$(n│distinct parts ,number of ODD parts is even ) Why is my iron ore disappearing when mined with a wooden pickaxe? I am on Peaceful mode, and I am using a Wooden Pickaxe. Whenever I mine Iron Ore, it just disappears. Am I doing something wrong? I'm an Indian. I'm planning to book a journey from Mumbai to Johannesburg, South Africa and back (conference visa). I looked at refundable tickets, while they are priced higher, they give you half your money back, for instance if the to and fro flight costs INR 40,000 they give you INR 20,000 . But this is if you are cancelling for some reason.   What if you have to cancel because your visa application or the transit visa application got rejected. As far as I understand the procedure is :-  a. Buy airline tickets   b. Apply for Visa   c. Wait between 1-6 weeks to get update about your visa application, for both visa and transit visa (although transit visa should be shorter I guess.)  d. If visa is granted then move on to planning other things about the trip.   Now in case, if the visa application fails (for whatever reason ) what recourse does the traveler have ?  Are there any airlines who are better understanding than others about this situation ?  In non-refundable tickets, I guess that all is lost or is there some way to save money there too.   Lastly, I read travel insurance can help in this case. How does travel insurance help in the above scenario ?  Edit :- One of the pre-conditions of getting the visa is   Proof of a Valid Return or onward ticket or purchase of ticket. This is from   and Example of a Borel set that is neither $F_\sigma$ nor $G_\delta$ I'm looking for subset $A$ of $\mathbb R$ such that $A$ is a Borel set but $A$ is neither $F_\sigma$ nor $G_\delta$. I have a bunch of raw data values that are dollar amounts and I want to find a confidence interval for a percentile of that data.  Is there a formula for such a confidence interval? Remotely changing hard drive boot order, windows 7 Probability of complete coupon set in $K$ boxes where a box has $N$ distinct coupons? Vector autoregression for mix of stationary and nonstationary variables I am currently investigating the impact of certain indicators such as GDP and inflation on the stock market. However some of my variables are non-stationary and some stationary in levels. All variables are stationary in first differences.  My question:   Since I have a mix of I(0) and I(1), I need to take the first difference of the I(1) variables and then use VAR. Say that I have a dependent variable $y$ which is I(0) and independent variables $x_1$ which is I(1) and $x_2$ which is I(0). Do I take the first differences of only $x_1$ and then apply the VAR model? Is that correct?  If I take the first differences, then might I lose the long-run relationship between the variables? Is ARDL the better method in this case?   If you have any references regarding the above I would be grateful. char!=(signed char), char!=(unsigned char) The code below compiles, but has different behavior for the char type than for the int types.  In particular     cout &lt;&lt; getIsTrue&lt; isX&lt;int8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;uint8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;char&gt;::ikIsX  &gt;() &lt;&lt; endl;   result in 3 instantiations of templates for three types: int8, uint8 and char. What gives?  The same is not true for ints: int and uint32 which result in the same template instantiation, and signed int another.  The reason seems to be that C++ sees char, signed char and unsigned char as three different types. Whereas int is the same as a signed int. Is this right or am I missing something?  #include &lt;iostream&gt;  using namespace std;  typedef   signed char       int8; typedef unsigned char      uint8; typedef   signed short      int16; typedef unsigned short     uint16; typedef   signed int        int32; typedef unsigned int       uint32; typedef   signed long long  int64; typedef unsigned long long uint64;  struct TrueType {}; struct FalseType {};  template &lt;typename T&gt; struct isX {    typedef typename T::ikIsX ikIsX; };   // This  int==int32 is ambiguous //template &lt;&gt;            struct isX&lt;int  &gt;    { typedef FalseType ikIsX; };  // Fails template &lt;&gt;            struct isX&lt;int32  &gt;  { typedef FalseType ikIsX; }; template &lt;&gt;            struct isX&lt;uint32 &gt;  { typedef FalseType ikIsX; };   // Whay isn't this ambiguous? char==int8 template &lt;&gt;            struct isX&lt;char  &gt;  { typedef FalseType ikIsX; }; template &lt;&gt;            struct isX&lt;int8  &gt;  { typedef FalseType ikIsX; }; template &lt;&gt;            struct isX&lt;uint8 &gt;  { typedef FalseType ikIsX; };   template &lt;typename T&gt; bool getIsTrue(); template &lt;&gt;           bool getIsTrue&lt;TrueType&gt;() { return true; } template &lt;&gt;           bool getIsTrue&lt;FalseType&gt;() { return false; }  int main(int, char **t ) {    cout &lt;&lt; sizeof(int8) &lt;&lt; endl;  // 1    cout &lt;&lt; sizeof(uint8) &lt;&lt; endl; // 1    cout &lt;&lt; sizeof(char) &lt;&lt; endl;  // 1     cout &lt;&lt; getIsTrue&lt; isX&lt;int8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;uint8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;char&gt;::ikIsX  &gt;() &lt;&lt; endl;     cout &lt;&lt; getIsTrue&lt; isX&lt;int32&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;uint32&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;int&gt;::ikIsX  &gt;() &lt;&lt; endl;  }   I'm using g++ 4.something I'm rewiring a a small part of a wall and I'm confused about a combination of the NEC and the products that I'm able to find.  I'm working on a 20 amp circuit (with 12g wire of course).  I'm connecting 4 receptacles each in their own box, 15 amp receptacles for normalcy.  But the terminals don't seem to accept 12g wire, even on the screws.  My first reaction was to make pigtails 14g pigtails, so that the 14g tap goes directly to the receptacle and is not used to feed the rest of the circuit.  12g in the box, 12g out of the box, and 14g inside the box only.    Is that type of splice allowed, or should I look harder for a 15 amp outlet that can more easily accept 12g wire?