This is my question. Black holes have infinite density right? (At least that is the leading theory), but if they have infinite density, and a finite amount of mass, then they must be infinitely small with means they can't have any volume. But that can't be possible because the definition of matter is anything with mass AND VOLUME. So that means black holes can't be made of matter because they are infinitely small, but they still some how have mass. I can't figure this out.
A singularity, by the definition I know, is a point in space with infinite of a property such as density.  Density is Mass/Volume.  Since the volume of a singularity is 0, then the density will thus become infinite because Mass/0 = undefined  However, is it possible to have a singularity with a mass of 0? 0/0 is indeterminate, but would it be possible for a singularity to exist even if its mass and volume were zero?
When will my phone get the Android 2.3 update (Gingerbread)? Difference between Can/Could: "Can (could) you sell your old computer to me?" What is difference between  Could you sell your old computer to me, seeing (that) you have no use for it. Can you sell your old computer to me, seeing (that) you have no use for it.  Can I use either one of them? Which one is grammatically correct or if both are, what is the difference in meaning? Creating Workflow -> Error What caused the oathbreakers in the Paths of the Dead to turn into shades? In Return of the King, we are told that the shades who populate the Paths of the Dead are the spirits of oathbreakers who refused to aid Isildur in the first fight against Sauron.  First, we are told of the oath (Book 5, Chapter 2):     But the oath that they broke was to fight against Sauron... For at Erech there stands a stands yet a stone that was brought, it is said, from Númenor by Isildur... and upon it the King of the Mountains swore allegiance to him in the beginning of the realm of Gondor.   Then, when they fail to honor the oath, we are told about Isildur's curse on them:     "...this curse I lay upon thee and thy folk: to rest never until your oath is fulfilled."   And as we see in the following chapters, the Sleepless Dead are indeed subject to this curse exactly as Isildur descibed it. What seems less clear, however, is how Isildur's curse manages to alter the fundamental nature of the oathbreakers' mortality, so that they became undead shades instead of simply dying in disgrace.   Do we have any other examples of Isildur performing similar acts of magic? Based on what we are told in LotR, Isildur appears to have been a great warrior, but not a regular practitioner of magic. Is the stone at Erech somehow magically involved? (If so, do we know anything more about it or how it works? Does its origin in Númenor have any significance?) It is mentioned that the oathbreakers had worshiped Sauron; could this be a clue? One image per overlay? What is the difference between ANSI/ISO C++ and C++/CLI? I want my intent to be launched when the user goes to a certain url: for example, the android market does this with  urls. so does youtube. I want mine to do that too. An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$ Most useful additions in KOMA-Script? (Background: I'm a beginner who will mostly use LaTeX for university articles and reports, but no math. Also, as I reside in Canada, the German typography conventions, which I understand KOMA-Script supports better than LaTeX, are less relevant).  I've read that the KOMA-Script package has a lot of improvements for the default document classes. Yet the 's length, about 250 pages, is somewhat daunting. I plan to read the chapters I'm interested in anyway but it'd be useful to have some pointers about low hanging fruits. I searched the site and  answers say KOMA-Script adds improvements but do not delve into details.  I'll ask this as a community wiki topic and, since the audience of this site is international, feel free to mention German typography if KOMA-Script is better there. How do I copy an entire directory into a directory of the same name without replacing the content in the destination directory? (instead, I would like to add to the contents of the destination folder) Why aren't hash values for "nothing" (empty) defined as all zeros? Any decent hash algorithm will produce basically "random like" values for any given input including the empty input.  For example MD5 produces d41d8cd98f00b204e9800998ecf8427e on an empty input.  I wonder, however, why the MD5 algorithm wasn't defined to have a final step where the output is XORed with d41d8cd98f00b204e9800998ecf8427e. This should not affect the cryptographic strength of the hash algorithm, and it would have the convenient property that a hash of all zeros represented a zero input.  Would it simply just because adding that step would slow the hash down a bit? To install the graphics driver I need to exit GUI / Gnome and go to the terminal. How can I do this in Ubuntu 18.04? Ctrl(STRG)+Alt+F1...F7 does not work, neither on the desktop, nor on the login screen... Prove that $\int_0^\infty \frac{x\,\log x}{(1+x^2)^2} = 0$ I have been asked to prove that $$\int_0^\infty \frac{x\,\log x}{(1+x^2)^2}\,dx = 0$$  I tried proceeding as follows: \begin{align} \int_0^\infty \frac{x\,\log x}{(1+x^2)^2}\,dx &amp;= \int_0^1 \frac{x\,\log x}{(1+x^2)^2}\,dx + \int_1^\infty \frac{x\,\log x}{(1+x^2)^2}\,dx \\ &amp; = \int_0^1 \frac{x\,\log x}{(1+x^2)^2}\,dx + \int_{u=1}^0 \frac{u\,\log u}{(1+u^2)^2}\,du\quad (\text{where }u=1/x) \\ &amp;= \int_0^1 \frac{x\,\log x}{(1+x^2)^2}\,dx - \int_0^1 \frac{u\,\log u}{(1+u^2)^2}\,du \\ &amp;=^? \int_0^1 0 \,dx \\ &amp;= 0 \end{align}  But I think that I should first show that the improper integral $\int_0^1 {x\,\log x}/{(1+x^2)^2}\,dx$ is convergent.  Do I need to show it? If yes, how to do so?  (I have been taught basic methods such as comparison, limit comparison and Dirichlet test.) How to execute code after html form reset with jquery? Ship an application with a database $|f(x)-f(y)|\geq k|x-y|$.Then $f$ is bijective and its inverse is continuous. My exercise says: Let $f:\mathbb{R} \rightarrow \mathbb{R}$ a continuous function e suppose that exists $k$ such that:  $$|f(x)-f(y)|\geq k|x-y|$$  Then $f$ is bijective and  its inverse is continuous.  Well, there's a Theorem , Invariance of domain, that says   "If $U$ is an open subset of $\mathbb {R^n}$ and $f : U \rightarrow\mathbb{R}$ is an injective continuous map, then $V = f(U)$ is open and $f$ is a homeomorphism between $U$ and $V$".  But I'm not knowing how to proceed...need a clue...Thanks for attention!!! I am trying to use netcat to send a simple message over TCP, e.g. I want to send the digit 1.  So I understood that I write the following in the terminal, after installing netcat  netcat [ip-address] [port]  But how do I specify the message to be sent? i.e. where to I write "1" ? Are there any method to extend a filesystem when i adding more hdd to it without using LVM? What are those ? Ball $X^*$ is weak-star metrizable iff X is separable in Conway's book. This is a Theorem in Conway's book     I don't understand in the third paragraph why there are open sets $\{U_n:n\geq1\}$ in $(ball X^*,wk^*)$ such that $0\in U_n$ and $\bigcap^{\infty}_{n=1}U_n=\{0\}$. By the definition of the relative weak-star topology on ball $X^*$, for each $n$, there exists a finite set $F_n$ contained in $X$ such that $$\{x^*\in\text{ball }X^*:|\langle x,x^*\rangle|&lt;1 \text{ for all }x\in F_n\}\subseteq U_n.$$  Can someone explain this for me？ Thank you so much!! System settings won't open on Ubuntu 20.04 LTS after adding System76/pop PPA I'm trying to open System Settings but it won't open in any way. Using GUI, Settings are trying to load for a moment and then they are gone. Using Terminal (gnome-control-center), I get: (gnome-control-center:8823): GLib-ERROR **: 14:44:15.433: ../../../glib/gmem.c:138: failed to allocate 13477064712 bytes Trap Trace/breakpoint (core dumped)  I tried: sudo apt-get remove gnome-control-center sudo apt autoremove sudo apt-get install gnome-control-center  With multiple reboots, but I had no result. UPDATE!: Same errors persist BUT, when I type: sudo gnome-control-center  (instead of just &quot;gnome-control-center&quot;) suddenly System Settings appear! Is it a user permissions issue? Any suggestions? UPDATE#2: After some system updates, sudo gnome-control-center now spawns &quot;Segmentation fault&quot;.