Does the age of the universe depend upon a specific choice of referential?
The age of the universe
sudo apt upgrade error 18.04 (Broken Packages) Normally, when a user edits one of my posts, I receive a notification like on the following depending on the case   User has editing privilege (click to visit revision)   Users' edit is submitted to review queue (click to visit review queue)     The above notifications were received instantaneously (or less than 30 minutes, in case caching is supposed to be the answer) as the edit was done/suggested.  But I did not receive any such notification today (yet) on an edit made on my . I think it is a possible bug and should be looked at. The recent notifications list I have is shown below: $\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}\in\Bbb Z\,\Rightarrow\, \dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}\in\Bbb Z$ Let $p,q,r$ be integers such that the symmetric sum of fractions $\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}$ is an integer. Prove that each of the numbers: $\dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}$ is an integer. How to do this? Someone posted but deleted soon. Wikipedia says that the name of concept comes from physics, but I cannot find any similarity between these two concepts. How to kill a player when they touch a block? I am making a multiplayer parkour map on bedrock edition, and I have it set up where when a player steps on a grass block they die. But when a player steps on a grass block it just kills anyone who touches it.  First: A repeat command block (set to always active and unconditional)   execute @e [type=player] ~ ~ ~ testforblock ~ ~-1 ~ grass   And then I have a chain command block (set to conditional and always active)  kill @e [type=player]   And it does work..... IF in singleplayer only. (which is not at all what I want)  Thank y'all in advance. WoeUSB Error Code 256 with NTFS formatted USB Is simply connectedness preserved after deleting a high codimension set Constructing a continuous function whose graph seems 'special' I've been reading through Zorich's "Analysis I" book recently, and I came across this nice little exercise.  Let $f: [0,1]\to \mathbb R$ be a continuous function such that $f(0)=f(1)$. Show that    for any $n\in \mathbb N$ there exists a horizontal closed interval of length $\frac 1n$ with endpoints on the graph of this function; if the number $\ell$ is not of the form $\frac 1n$ there exists a function of this form on whose graph one cannot inscribe a horizontal chord of length $\ell$.   The first part can be proven like this: Consider $g: [0,(n-1)/n] \to \mathbb R$ given by $g(x) = f(x) - f(x+1/n)$. Then   $$\sum_{k=0}^{n-1} g(k/n) = 0$$  and therefore either all of these points are zero or there exists both a point where $g$ is positive and a point where $g$ is negative. By continuity, there must then also be a point where $g = 0$. So we are done.  Now, the second statement seemed rather counterintuitive, and I have given it some time now, but don't see a counterexample for $\ell &lt; 1/2$.  (For $\ell &gt; 1/2$ the function $f(x) = \sin(2\pi x)$ will do.)  Can anyone help me out?  Cheers, I'm sorry if this question goes against the meta for posting questions - I attached all the "beware, this is a soft-question" tags I could.  This is a question I've been asking myself now for some time. In most areas, there's a "cut off age" to be good at something. For example, you're not going to make the NHL if you start playing hockey at 20. It just won't happen.  So my question then, how late is too late to start studying math and make a career out of it? By "start studying math" I mean, to really try to understand and comprehend the material (as opposed to just being able to do well in a formal, intuitional environment).   I don't mean this from a "do what you love, its not too late" motivational perspective. I mean this from a purely biological perspective; at approximately what age has your brain's capacity to learn effectively and be influenced by your learning stop? When does the biological clock for learning new math run out?  My reasoning for asking this question is (for those who care): I love math. Really I do. But , having spent the first 21 years of my life in sports/video games/obtaining a degree in a scientific field which I care nothing of/etc, despite all my best attempts at trying to learn math, am I just too late starting to ever actually be good enough at it to make it a career? I've almost completed my second degree (in Math), but find that in many cases, despite how I look at a problem, I lack the intuition to comprehend it. I'm going to single him out (sorry), only as an example, but Qiaochu Yuan is my age.   Note 1: If this question isn't a suitable post, I won't be offended at all if you vote to close - I know this question borders what's acceptable to ask.  Note 2: Thanks to everyone for reading and taking the time for the great responses. Really appreciate it! Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$ Show that $$\lim_{x \to \infty} \frac{\log(1 + e^x)}{x} = 1$$ How do I prove this? Or how do we get this result? Here $\log$ is the natural logarithm. If $AB = I$ then $BA = I$ Optimizing logical sector size for physical sector size 4096 HDD With many new hard drive disks the physical sector size is 4096. Would it be possible to make the system use a logical sector size of the same size, rather than the default logical sector size of 512?  Will it speed up bulk reads and writes? Where can it be configured? Lightning QuickAction (API) without modal I am attempting to replace JS buttons with quick actions. These button simply call a web service method and alert the result and need no user interaction.  With quick action a modal always seems to appear and this is not desirable.   I am calling the Webservice method in the doInit function and  firing a toast event with the results and have no need for the modal popup.  Seems an oversight maybe? But is there a way to accomplish this without the modal to closely mimic the JS button functionality?  Ideally we could show the spinner without the modal   Right now I am simply calling   $A.get("e.force:closeQuickAction").fire();   at the end of the doInit but it is not the most ideal in way of a UI to do this IMHO as it flashes the modal on the screen briefly. I currently have an Ubuntu-Windows Dual boot. However, I would like to try out a new OS so I burned Linux Mint to a USB stick.   I would like to install Linux Mint and remove Ubuntu while still keeping my windows dual boot. I've already backed up my Ubuntu setup so I can wipe it out.   In the Linux Mint installer, should I choosing the "install alongside windows" option do this? This is a question in Ahlfors in the section on the argument principle: How many roots of the equation $f(z)=z^4+8z^3+3z^2+8z+3=0$ lie in the right half plane?  He gives a hint that we should "sketch the image of the imaginary axis and apply the argument principle to a large half disk."  Since $f$ is an entire function, I think I understand that the argument principle tells us that for any closed curve $\gamma$ in $\mathbb{C}$, the winding number of $f(\gamma)$ around 0 is equal to the number of zeros of $f$ contained inside $\gamma$.  How would you go about actually applying the hint though? I am having trouble figuring out what the image of a large half disk under $f$ would look like. Which is the simplest way to update a Label from another Thread?   I have a Form running on thread1, and from that I'm starting another thread (thread2).  While thread2 is processing some files I would like to update a Label on the Form with the current status of thread2's work.   How could I do that? Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ if $m &lt; 0$. This statement came up in an algebraic geometry text with no explanation provided, and I'm trying to understand why it's true.   Thoughts so far:   Since $H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m))$ is the vector space of regular sections of $\mathcal{O}_{\mathbb{P}^n}(m)$ over $\mathbb{P}^n$, we can try to find a basis. Since the regular sections are the degree $m$ polynomials in $x_0, \dots, x_n$, it seems like the collection of degree $m$ monomials in $x_0, \dots, x_n$ should work. But I don't see how there are ${n + m \choose n}$ of these. Is it just a basic counting argument that I'm struggling with?  On a side note, I think I understand what global sections of $\mathcal{O}_{\mathbb{P}^n}(m)$ look like, but how can we describe the regular sections over a distinguished open set $D(f)$? Is it something like degree $m$ polynomials with denominator $f$? Block computer from joining a domain if it has the same name as another computer object in ADUC A user has asked  which did not receive much attention, and thus the user deleted the post. After some time, the user asked the  (with just slight changes to the title and a tag change), so that it could receive a bit more attention. The strange thing is that the question was not downvoted or poorly written, and yet the user deleted the original post. Now, since the original question was deleted, I could not mark the new one as a duplicate (it threw an error). My question is, how do we handle such questions? Just let them be as such or let the user know about it or is there another way to handle such situations? Change the location of saved screenshot when screenshot taken by printscreen button in GNOME 3