On my Math.SE account, it says "user was removed" and 5 reputation was deducted. What does this mean?
Message appearing when a user was removed.     It seems I lost 1765 reputation points on Stack Overflow yesterday. The reason given in my history is "removed", with the description of "User was removed ()". I don't understand what that means. What caused this?
Links being changed to cppreference.com Someone just edited a link in one of my answers to point to a 'better reference'.    I've no problem with links being changed in general, but this smells like part of a concerted attempt to redirect traffic.   Is this kind of activity acceptable on SO? Community user id interpreted by absolute value in search Take a look at this example schematic:  The chip in question is the  and as you can see power is provided on both sides (with a 100nF cap to smooth noise I guess). Is this strictly required or could you put power into one side and just ignore the other? I know that I have just put power in one side and everything still seems to work fine but I feel uneasy with doing that. I feel that they would not waste pins that could be doing something useful by having an extra pair of power in/out pins. For what purpose does this PIC MCU (and others like it) have multiple power pins? Irreducible polynomial of degree $8$ My question is in the title. I'm a little lost in how to solve this problem. There is a hint associated with the problem that states the following:   Use a line integral to show that $ |f(z)| \leq A + |z| $ where A = $\max\{1, |f(0)|\}$  Thanks for the help. Output to stdout and at the same time grep into a file Why are integer GCDs positive? [unit normalization of GCDs] The definition in my text reads, An integer $d$ is said to be the greatest common divisor of two non-zero integers $a$ and $b$ iff,  $d|a$ and $d|b$ and if $k$ is any other common divisor of $a$ and $b$ then $k|d$  Now here's the thing, if $d|a$ and $d|b$ then surely $-d|a$ and $-d|b$ as well, also $k|-d$ What I take from this? GCD is not unique! That is if $\mathrm{gcd}(12,8)= 4$ then by the definition, $\mathrm{gcd}(12,8) = -4$ as well. Yet I never ever seen a negative gcd. Someone please explain. Maybe, $4&gt;-4$, and we want the &quot;greatest common factor&quot; so...? But that still doesn't justify the definition. Lost my APFS partition after using EaseUS partition manager on Bootcamp I used macOS mojave(APFS partition) and Windows10(Bootcamp). And I tried to expand Bootcamp partition with moving Windows OEM partition by EaseUS partition master in windows. After this, I can’t find APFS partition installed macOS.  I use MacBook Pro 2016.  I think “disk0s2” was APFS partition, but now it is “Windows Recovery” partition.  Do you have any ideas to solve this? (I am Japanese, so I'm sorry for my poor English)  I tried “gpt show” and “diskutil list” on macOS Recovery   Additional information  I tried dd if=/dev/disk0s2 count=1 bs=512 command in a Terminal app of macOS Utility from network boot, and the terminal says,  -bash-3.2# dd if=/dev/disk0s2 count=1 bs=512 | vis -c 1+0 records in 1+0 records out 512 bytes transferred in 0.005472 secs (93568 bytes/sec) )us??-ҵ?\^A\0\0\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^A\0\0\M^@\0\0\0\0NXSB\0\^P\0\0?\M^B?\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\^B\0\0\0\0\0\0\0"\^R???\M^_@}\M^Bvy57 ?(h?8\0\0\0\0\0?\M^F\^Z\0\0\0\0\0\^X\^A\0\0 l\0\0?\M^J\0\0\0\0\0\0\^R\r\0\0\0\0\0\0\a\0\0\0004*\0\0\^E\0\0\0\^B\0\0\0\^S*\0\0!\0\0\0\M^Qr8\0\0\0\0\0\M^U?\b\0\0\0\0\0\^A\^D\0\0\0\0\0\0\0\0\0\0d\0\0\0\^C\^D\0\0\0\0\0\0\M^T\M^N\^A\0\0\0\0\0\M^V\M^N\^A\0\0\0\0\0?0\^B\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0-bash-3.2#   . Lille Metro schedule... is it 24/7? The M1 and M2 lines in Lille, France have a confusing . It's 7 days per week, but it looks like it's "running" basically 24h hours per day (minus some ten-minute delay). I never took the metro later than 11 PM when I was in Lille last year, but people told me that it stops just before midnight. But... it looks like it starts right back up again immediately, after about 10 minutes.  What are the actual hours of the Lille M1 and M2 lines? I have a hard time believing that they're 24/7... Blender render crash when using subsurf modifiers. solving diophantine equations using congruences So, a question in Elementary Number Theory by David M. Burton:     Problems 4.4      2(a) Using congruences, solve the diophantine equation 4x + 51y = 9       Hint: $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$, whereas $ \ 51y \equiv 9 (mod \ 4)$ gives $y = 3+4s $. Find the relation between $s$ and $t$ From this hint, I substitute $ x = 15 +51t$ and $y = 3+4s$ in the given equation $4x + 51y = 9$ to get the relation $s = -t-1$ and using which I can get the solutions $ x = 15 + 51t, \ y =-1-4t$ But we know that the solutions of $ax \equiv b (mod \ n)$ is equivatent to the solutions of the diophantine equation $ax -ny = b$, so, solutions of $4x \equiv 9(mod \ 51) $ is equivalent to solutions of the equation $4x-51y=9$ whereas, solutions of $51y \equiv 9(mod \ 4) $ is equivalent to solutions of the equation $-4x+51y=9$ Now, my question is: as, the above equations $4x-51y=9$ and $-4x+51y=9$ are different, then what is the point of substituting $ x = 15 +51t$ (solution of $4x-51y=9$) and $y = 3+4s $ (solution of $-4x+51y=9$) in the given equation $4x+51y=9$ to find a relation between $t$ and $s$ ? Isn't it absurd as $ x = 15 +51t$ and $y = 3+4s $ are solutions of two different equations? Can anyone please explain this? PS: I did it like this $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$ and by substituting it in $4x+51y=9$ we get $y=-1-4t$ Probability associated with experiencing all outcomes SVG donut slice as path element (annular sector) What solutions does the equation $4x\equiv2\mod10$ have? (Hint, it will have more that one.) What about solutions to an equation $ax\equiv d\mod n$, where $d=\gcd(a,n)$?  This is the question that appeared in our universities last year paper. But it seems very difficult for me like for first part I am able to solve by simplifications I got $x=5\cdot Z +3$ as solution which makes sense and seems fair but for the second one, I have no idea how can I approach that. Can you please help me out with that one. I tried to simplify that by using Euclidean algorithm but still, I didn't get any idea that what actually the solution will be. My final exam is on 2nd of next month and because of covid I am unable to contact in person for any help. So any help from this site will be appreciated. Thank you for looking at this question! Can't boot without Flash Drive plugged in How can magnets be used to pick up pieces of metal when the force from a magnetic field does no work? I learned that the force from a magnetic field does no work. However I was wondering how magnets can be used to pick up pieces of metal like small paperclips and stuff. I also was wondering how magnets can stick to pieces of metal like a refrigerator? This is my first question.   Let $a_1, a_2,\ldots, a_k$ be natural numbers $\leq n$ with $m$ prime factors.  Let $p_1, p_2, \ldots, p_r$ be the prime numbers $\leq n$.   Let $$C_{m,n} = \frac{\sum_{i=1}^{k}a_i}{\sum_{i=1}^{r}p_i}$$ Does the following limit exist when $m\geq 2$? Obviously, when $m=1$,  $C_{1,n}=1$.  $$\lim_{n\to \infty} C_{m,n}$$  I have some guesses but not defendable enough.  My best,  The FM. I was pondering a bit more about  question regarding being able to &quot;omit&quot; the base case in a proof by strong induction due to vacuous truth. The post states:  Strong induction proves a sequence of statements $P(0), P(1), …$ by proving the implication &quot;If $P(m)$ is true for all nonnegative integers $m$ less than $n$, then $P(n)$ is true.&quot; for every nonnegative integer $n$. There is no need for a separate base case, because the $n=0$ instance of the implication is the base case, vacuously.  However, if we consider $n=0$, we would have that the statement is vacuously true, which I would take to mean that the implication is true regardless of the validity of $P(0)$. However, clearly it's necessary for $P(0)$ to hold for an induction proof to be valid. So I'm confused on how, by omitting the base case, $n=0$ isn't just a tautology, making the implication true regardless of whether $P(0)$ actually holds. The impression that I got from the  films was that if  was successful, most of the world was going to suffer greatly. Basically everyone would serve Voldemort as slaves or die. So what's the point of serving someone who's probably going to ultimately end up betraying and/or enslaving you? I know the  hated , but is that really enough to justify tearing down Wizard society? Why exactly do the Death Eaters serve Lord Voldemort? Fear? Is the post-Voldemort world not that bad? (I for one welcome our ) Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions. (Reference : Fraleigh, A first course in abstract algebra)     Prove that a nonempty set $G$, together with an associative binary operation * on $G$ such that $a*x=b$ and $y*a=b$ have solutions in G, $\forall a,b\in G$, is a group.   Because * is an associatie operation, we have to prove that: there exists $e\in G$ such that $e*a=a=a*e$ for any $a\in G$, and that for any $a\in G$ there exists $\alpha \in G$ such that $a*\alpha=e=\alpha *a$.  This is very confusing, first I tried to prove the identity exists. If we consider a=b, then $a*x=a=y*a$, and because of the hypothesis $x,y\in G$ always exists, now we have to show that $x=y$, but I just can't do this with out inverses, so I tried to prove that the inverses exists, however I have no idea how the identity looks like, I'm stuck.  And I tried to get unstuck, so I thought particular cases, first if $G$ had only one element, then what would happend if it had just two elements... but I remembered that we don't know if G is finite or not, and I think this makes things a little bit more complicated.  What can I do?