I have an 8 TB disk in my Mac. I had 2 APFS containers on it (disk7 and disk8). After deleting APFS container disk8, I get this:  The space that the deleted APFS container disk 8 used up is lost and not reclaimed by APFS container disk 7. I tried  diskutil apfs resizecontainer disk5s1 0, but no result. I can only use 4.3 TB of my 8 TB disk. How can I make container disk 7 use all 8 TB? sudo gpt -r show /dev/disk5
Last login: Mon Jun  7 22:43:40 on ttys000 samadams@Sams-MacBook-Pro-2 ~ % diskutil cs list No CoreStorage logical volume groups found samadams@Sams-MacBook-Pro-2 ~ % diskutil list /dev/disk0 (internal, physical):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      GUID_partition_scheme                        *121.3 GB   disk0    1:                        EFI ⁨NO NAME⁩                 536.9 MB   disk0s1                     (free space)                         60.5 GB    -    2:                 Apple_APFS ⁨Container disk1⁩         60.1 GB    disk0s2  /dev/disk1 (synthesized):    #:                       TYPE NAME                    SIZE       IDENTIFIER    0:      APFS Container Scheme -                      +60.1 GB    disk1                                  Physical Store disk0s2    1:                APFS Volume ⁨MacOS Big Sur - Data⁩    30.0 GB    disk1s1    2:                APFS Volume ⁨Preboot⁩                 233.2 MB   disk1s2    3:                APFS Volume ⁨Recovery⁩                652.6 MB   disk1s3    4:                APFS Volume ⁨VM⁩                      1.1 GB     disk1s4    5:                APFS Volume ⁨MacOS Big Sur⁩           24.4 GB    disk1s5    6:              APFS Snapshot ⁨com.apple.os.update-...⁩ 24.4 GB    disk1s5s1    7:                APFS Volume ⁨Untitled⁩                860.2 KB   disk1s7
Quantum entanglement faster than speed of light? recently i was watching a  on quantum computing where the narrators describes that quantum entanglement information travels faster than light!  Is it really possible for anything to move faster than light? Or are the narrators just wrong?  Regards, Suppose $u\in W^{1,1}$ and $\partial u$ is $C^1$. I want to prove the following: $$\int_{\partial\Omega}|u-\bar u|\leq A\int_{\Omega}|\nabla u|$$ where $\bar u=\frac{1}{|\Omega|}\int_{\Omega}u$ and $A&gt;0$. Note that unlike Poincar&eacute; inequality, the left integral is over $\partial\Omega$ and not $\Omega$. How can I do that?  I tried to prove in a similar way to Poincare inequality proof (arguing by contradiction), but with no success. I think I am missing something because of the  $\partial\Omega$ issue. Death in SAO before Kayaba announcement I was wondering if in the novel we knew about some deaths occurring before Kayaba announcement. I remember that in the anime, Kirito plays a bit with Cline before realizing that the log off option has disappeared. Then all the people are summoned to the city and learn about the fact that if they die in the game, they also die in real life.  I don't remember any players dying before the announcement in the anime, except for those who are not waking up and their relative pulling off their NerveGear thus causing death, but maybe in the light novel, some guys died without even knowing it just while being defeated by a mob (which seems awful for me).  Do we know about some players dying before that while thinking they are still in a normal game? Suppose Alice chooses a random Prime $p$ and a random private Key $a \in \mathbb{Z}^*_p$. By accident, she also chooses a random number $g \in \mathbb{Z}^*_p$, which is not a generator of $\mathbb{Z}^*_p$ and therefore  $$\langle g\rangle \subset \mathbb{Z}^*_p$$  as opposed to $\langle g\rangle = \mathbb{Z}^*_p$, which would yield a valid key. Alice then computes $A \equiv g^a \pmod{p} $ and publishes the Tuple $(p,g,A)$ as her public key.  Bob now encrypts a message $M$ using Alices public key by computing  $$C_1 = g^b \pmod{p}$$ $$C_2 = M \cdot A^b \pmod{p}$$  Is it possible for an attacker (Eve) to distinguish a “real” ciphertext $(C_1,C_2)$ from a random ciphertext $(Z_1,Z_2) \stackrel{$}{\longleftarrow} \mathbb{Z}^*_p$ with significant advantage (say $Adv \geq \frac12$)?    Edit: I guess it should be enough to show, that the ciphertext cannot be random, if  $$\langle g \rangle \neq \langle C_1 \rangle \quad(\text{or $Z_1$, respectively})$$  But how can Eve check for this property efficiently? Can someone point me in the right direction here?    Edit: A real-world situation where this flaw occurred Branch of the n-th root of a holomorphic function is holomorphic It is true that given a domain $D$ and a function $f$ that is holomorphic and not vanishing in $D$, then a branch $\varphi$ (with $\varphi$ continuous) of $f^{1/n}$ in $D$ is holomorphic in $D$ ().   My question is, does the statement remain true if we remove the non-vanishing condition? I haven't been able to find a counterexample or a proof on that more general case. How can you prove that the square root of two is irrational? Let $t\in \mathbb R$. Prove that $\displaystyle{\sum_{n=1}^{\infty}n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+t}$ converges iff $t=\frac{1}{6}$.  While the $(\Rightarrow)$ direction was fairly easy (as $a_n$ should converge to $0$, forcing $t=\frac{1}{6}$), i'm facing some hard time trying to prove the second direction, that is $\displaystyle{\sum_{n=1}^{\infty}(n^{3}\sin\left(\frac{1}{n}\right)-n^{2}+\frac{1}{6})}$ converges. I did notice that $a_n=a_{-n}$ and tried to write this series as a Leibnitz series, but had no luck since the sequence doesn't decrease. I also tried to prove absolute convergence but then again, no luck. Thanks. Concatenating string with space How does an attacker's reach interact with the Mounted Combatant feat's ability to force an attack against the mount to target the rider instead? Misplaced navigation bar and question title It appears that on Server Fault and Super User, the navigation bar and question title have suddenly become misplaced. The same does not occur on SO and mSO, nor on any of the other SE sites I spot-checked.  This is being seen in both Chrome and Firefox and just began occurring within the last few minutes.      What it should look like:      While this was fixed for a few hours, it has returned as of 22:05. Using indefinite articles before adjectives: "Let's have a good breakfast" Let's have breakfast    Let's have a good breakfast      I've learned that indefinite articles aren't used before uncountable nouns, so why is a used before the adjective "good" here?    Is there an exception to the rules or is it wrong? How to shrink Windows 7 boot partition with unmovable files Here's what is happening; everytime I go to Stack Overflow (stackoverflow.com, NOT meta) with Firefox, it gives me the "Welcome back" tab that pops up from the top. Whenever I click in the "click here to refresh the page" link, all it does is refresh the page without logging me back in.  Even if I try to log in using the "log in" button at the top, all it does is pop up the tab that says "Welcome name here, you're being redirected." The problem is I'm not being logged in, not to mention that it keeps refreshing the page over and over again without giving me a choice to log in with Facebook.  For some reason, I was capable of logging in to Meta Stack Overflow using Firefox. I am still unable to log in to Stack Overflow. Any ideas? How to get product recommendations Finding the asymptotic of an integral I came across the following exercise on asymptotic behavior of integrals: $$I(a) = \int_0^\infty\frac{\cos x}{x^a} \, dx, \text{ where } a\to0^+.$$ I have tried integrating by parts or replacing $\cos x$ with the first summands of its Taylor series, but I end up with something equal to infinity (independent of $a$ and that is not what we want).  I just thought about the substitution $x \leftrightarrow\frac{1}{1+x^2}$ and I get the  following result:  $$I(a) = \frac{\cos(1/2)}{2^{2-a}} + \int_0^1\frac{2x^3 \cos\left(\frac{1}{1+x^2}\right)}{(1+x^2)^{3-a}} \, dx - \int_0^1 \frac{2x^3\sin\left(\frac{1}{1+x^2}\right)}{(1+x^2)^{2-2a}}\,dx$$ If I could prove that the last summands are $o(I(a))$ then it would be OK, but I think, in general my strategy won't work. Apparently this is supposed to be an easy exercise, but I can't come up with anything right now. Can I programmatically open the devtools from a Google Chrome extension? How do I run a sudo command in Emacs? Why (in relatively non-technical terms) are Calabi-Yau manifolds favored for compactified dimensions in string theory? How to convert Bedrock texture pack to Java Edition Minecraft Value of the Hubble parameter over time There is something I don't understand about the  $H$, as it seems to clump two concepts together that I can't quite unify in my head. On the one side, we have  $$V = D H$$  which means that for a given distance $D$, there is a certain amount of new space created over time - and $H$ is simply the factor that makes this relationship work. So, for example, say we have two points 1 Mpc apart, this would mean they recede at about 70 km/s away from each other  (given our current approximation of $H$).  Now the thing I can't wrap my head around is that   $$T =\frac{1}{ H}$$  is also the age of the universe. Contrary to claims made on, say, Wikipedia this means that $H$ cannot possibly have been a constant throughout the past 13 billion years, because mathematically $1/H$ means that $H$ must be continually shrinking as the universe ages.  So if $H$ did start out as some huge value and is now shrinking over time, doesn't this mean the expansion of the universe is slowing down? Because if $H$ is shrinking, I'll get a lower value of $V$ today than I'll get tomorrow. Shouldn't the notation then be more like  $$V = DH(t)$$  So which one is it? If $1/H$ is simply the solution for $D=0$, how can we use it as the expansion-velocity-per-unit-of-distance at the same time? What's worse, how can literature say $H$ has probably been more or less constant forever and simultaneously assert that $1/H$ is the current age of the universe? What am I missing?