Is there a word for the totality of existence?
Word for "things which exist"
I am wondering, given the minimal polynomial of $A$, what can we say about the minimal polynomial of $A^n$?  I know that if we were looking at the roots of the characteristic polynomial ie eigenvalues then the roots of the characteristic polynomial of $A^n$ would be $nth$ powers of the eigenvalues so again these are roots of the minimal polynomial also. Proofs of consistency for two formal systems Do there exist two formal systems, $F_1$ and $F_2$, such that $F_1$ proves $F_2$ is consistent and $F_2$ proves $F_1$ is consistent?  Would these proofs bypass Gödel's Second Incompleteness Theorem?  By "consistent", I mean the formal system does not prove $X$ and NOT $X$. How can I prove this sequence is decreasing? My problem is how to prove  $$\frac{1+2}{1}  &gt; \frac{1+3+\frac{3^2}{2!}}{1+2} &gt; \frac{1+4+\frac{4^2}{2!}+\frac{4^3}{3!}}{1+3+\frac{3^2}{2!}}&gt;\cdots $$  i am sure that the sequence is decreasing as limit exp(1).  However, the reason why the sequence is decreasing is not evident.  Thanks if you consider this issue and make me relief. How can I turn off the shrine indicator (or make it stop beeping)? How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once? Background: I'm working on  for , and I've run into a problem with how I'm creating the individual matchups (groups of 4 entries).  Currently, I'm simply generating all combinations of 4 elements (in the combinatoric sense) of entries, but that gets really big really quickly:  $$x \choose 4$$    (from )  Therefore, my question is: How can I choose subsets (of length $n$) of a set such that each element of that set appears in the same subset as every other element at least once, while maintaining a minimal amount of subsets?  I can figure this out for $n = 2$, since the solution is quite intuitive: simply combine the first element with every other element, combine the second element with every other element that comes after it, etc. For a set of length $L$, this yields:  $$\sum_{x=1}^{L-1}(L - x)$$    (from )  which is much smaller and more manageable.  However, I still have not been able to figure out: How can I generalize this to any $n$? Purpose of @ Symbol Before Strings? How did Thanos know about the power of "The Snap"? In the scene on Titan with Doctor Strange in Avengers: Infinity War, Thanos said,     With all six Infinity Stones, I will simply snap my fingers and it would all cease to exist.   Then again, in the very first scene with Thor and Loki, when Maw gave Thanos the Space Stone, he said that no one has ever worn two Infinity Stones together.   So how come Thanos knew about the power of the Snap? Because as Wong puts it to Tony, the Big Bang hurled the six Infinity Stones across the universe.   So if no one had collected all the six stones before Thanos, then how did he know about the ability to "Snap"? Continuity of $f(x)$ on $[a,b]$ implies continuity of $f(t) = \displaystyle \min_{a \leq x \leq t}f(x)$ at [a,b]. I am sure there is something wrong i am doing but i just want someone to point it to me.  Why can't we say that $e^{\frac {\pi i}{3}} = \left(e^{\pi i}\right)^{\frac {1}{3}} = (-1)^{\frac {1}{3}} = -1$ Why do we have to calculate it by the formula as it is (which produces different value)  Another question is why can't we say that $ (-1)^{\frac {1}{2}} = \left(\left (-1\right)^{2}\right)^{\frac {1}{4}} = 1^{\frac {1}{4}} = 1$  Again i have to say that i know this is all wrong i just want to know why it is wrong Deleting Lines Containing a Specified String in Different Files Suppose there are two files in web/ named foo.php and bar.php. The 1st line of foo.php is "sdajgeSTRINGdsad" and the 10th line of bar.php is "gdfhu98324STRING". The task is to first locate these two files, then delete 1st line of foo.php and 10th line of bar.php given that the specified string is "STRING". "Important to me" or "Important for me" I cannot easily figure out which one is more appropriate to use:     It's important to me.        It's important for me.   Are they the same? If not, what's the difference? When to use Stateful session bean over Stateless session bean? Goal: I want to be able to securely use the internet via my home PC while my notebook is connected to an open hotspot/access point.  I do know that I can use a SSH tunnel/SOCKS proxy, but I don't want to fiddle around with applications (making them use it, if even possible). I guess what I need is an OpenVPN setup, so I'm looking for a detailed guide on how to:   Install and setup the OpenVPN server Setup the OpenVPN client (NetworkManager)   Ubuntu versions this should work on are 10.10 and 11.04. Is there a word to describe words that can be spelled different ways? Is there a word in English to describe words that can be spelled more than one way?  For example:   colour and color favourite and favorite   However, this shouldn't be limited to words spelled differently in different dialects, though I'm not sure what other case there would be. As of the November 2018 core book updates, what changes were made in the latest printings of the PHB that aren't noted in the errata document? Boy goes insane during space travel I'm trying to remember the name of a short story I read about 25 years ago or so. I'd also like to know of any collections it appeared in.   The details I recall involve a family who are embarking on a hyperspace journey. To undertake this journey you have to be put to sleep. One of the children pretends to be asleep, and when the jump is complete the child has gone insane. From the child's point of view the jump lasted for an eternity while in reality it was only a few seconds. I know there are many ways to prevent image caching (such as via META tags), as well as a few nice tricks to ensure that the current version of an image is shown with every page load (such as image.jpg?x=timestamp), but is there any way to actually clear or replace an image in the browsers cache so that neither of the methods above are necessary?  As an example, lets say there are 100 images on a page and that these images are named "01.jpg", "02.jpg", "03.jpg", etc. If image "42.jpg" is replaced, is there any way to replace it in the cache so that "42.jpg" will automatically display the new image on successive page loads? I can't use the META tag method, because I need everuthing that ISN"T replaced to remain cached, and I can't use the timestamp method, because I don't want ALL of the images to be reloaded every time the page loads.  I've racked my brain and scoured the Internet for a way to do this (preferrably via javascript), but no luck. Any suggestions? I tried to write out the aura if statement but I am getting stuck if someone can explain it to me in detail. thank you  &lt;aura:if isTrue=&quot;{!lessthan(v.Tl.time, v.Tl.End_Date_Time1__c)}&quot;&gt;                            &lt;/aura:if&gt; How can I change xfce bottom panel to the top? I am using Xubuntu 12.10 and would like to change the panel which is currently on the bootm to the top.  This is the opposite of what most people using Unity want to do.    I have done this in the past but have forgotten how and could not find the info easily this time. Cheers, How to boot WUBI installed Ubuntu within Windows 8?