Show from the definition of a Cauchy Sequence that Xn=ln(n) is not a Cauchy Series
I read in the book Applied Analysis by Hunter and Nachtergale that     the sequence $x(n)=\log(n)$ is not Cauchy since $\log(n)\to\infty$   But that seems to be irrelevant to the definition of a Cauchy sequence which I understand is as follows:     A sequence $x(n)$ is said to be Cauchy if for every $\epsilon &gt; 0$  there exists an $N$ such that $\lvert x(m)-x(n)\rvert &lt; \epsilon$ for all $m,n&gt;N$.   This sequence $(\log n)$ seems to meet the definition. So how come it is not considered Cauchy?
i keep getting the script error problem every time i try using polygon to raster tool in ArcGIS 10.1. Please help me how I can solve this?  screenshot embedded Does Dim Light created by an effect override Bright Light in an area? Two examples.     A silvery beam of pale light shines down in a 5-foot-radius, 40-foot-high cylinder centered on a point within range. Until the spell ends, dim light fills the cylinder.      —Moonbeam, Player's Handbook, pg. 261        You create up to four torch-sized lights within range, [...] each light sheds dim light in a 10-foot radius.      —Dancing Lights, Player's Handbook, pg. 230   Now consider that each of these spells are cast on a bright day, obviously covered by Bright Light, as the game understands it.   Do these spells change the Bright Light within the area affected by them into Dim Light? Is the behavior different between Moonbeam ("Dim Light fills the cylinder") and Dancing Lights ("each light sheds dim light"), or do both of them behave the same? The 's  feature (E:RftLW, p. 58; WGtE, p. 180) states:     [...] You ignore all class, race, spell, and level requirements on attuning to or using magic items.   Class and race requirements are relatively intuitive, additionally, since an Artificer is able to cast spells they can already attune to items that require you to be a spellcaster. But there's still some questions:   Can they use a spell scroll of a spell not on their spell list? Is this one of the four requirements ignored? What are level and spell requirements; what are some examples? Lets say an object is tied to a string and it is being swung in a circle:    In this case, the tension of the string acts as a centrifugal force that keeps the object moving in a circle. However, if centrifugal force is the only force acting on the object, why doesn't it collapse into the center? I am pretty sure this has to do with the object's inertia (or the centrifugal pseudo-force), where it moves slightly forward in a tangent before falling, restoring the orbit.  Also, what keeps the string taut during the swinging? There has to be some force countering the centripetal force that keeps the string tight. I think this might again have to do with the intertia/centrifugal pseudo-force but can a pseudo-force balance a real force? Also, if centripetal were to be balanced by the pseudo-force, wouldn't the object not move at all (since the net force would be 0)? What can I do if my USB flash drive is write-protected or read-only? SUID-bit not working for executables within /tmp directory Printing the value of getuid() and geteuid() from an executable with SUID-bit (chmod +s) turned-on, seems to result with the original caller ID instead of the owner id if the executable is located within the /tmp directory.  When compiling the exact same code to home directory (and executing chmod +s), this seems to work as expected.  I've searched a lot and could not find any reference to such behavior.  Does anybody know why is this happening?  this source is simple as that:  #include &lt;stdio.h&gt; #include &lt;stdlib.h&gt; #include &lt;sys/types.h&gt; #include &lt;unistd.h&gt;  int main(){     printf("%d\n%d\n", getuid(), geteuid());     return 0; } When trying to deploy the converted metadata using VS code sfdx force:mdapi:deploy deploy to my Production Org and I get the error Property 'itemInstances' not valid in version 48.0 and Property 'processOrder' not valid in version 48.0. But when I go to Developer Console and open a class, even though it says 48.0, I have the option to select 49.0, so I am assuming I have 49.0. Yet I get this error. Pretty much all my classes, trigger and components are version 48.0, but I am not sure how that affects flexipages and Approval processes. number of subsets of even and odd Compact subset in colimit of spaces How can I create a zip archive of a whole directory via terminal without hidden files? I have a project with lots of hidden folders / files in it. I want to create a zip-archive of it, but in the archive shouldn't be  any hidden folders / files. If files in a hidden folder are not hidden, they should also not be included.  I know that I can create a zip archive of a directory like this:  zip -r zipfile.zip directory   I also know that I can exclude files with the -x option, so I thought this might work:  zip -r zipfile.zip directory -x .*   It didn't work. All hidden directories were still in the zip-file. Can I still use the older Airport Utility 5.5.3 if I install the 6.0 version of Airport Utility? Looking for a book I read in the 90's (not sure if it was published in the 90's or not).  The story as far as I can remember goes like this. Human-looking aliens evolve on a very hostile planet. They encounter some big bad threat and they cast about for help. They encounter a rich industrialist on Earth and they send a woman to recruit him. She teaches the guy to use magic and how to transform his body. They build a ship and travel to her planet but just before they arrive, she vanishes and he crash lands on this hostile planet.  He goes through many trials and tribulations in order to get to her and eventually he has enough and uses the ability she teaches him on how to transform his body. He transforms himself into a half-man, half-dragon-like creature which allows him to travel to the other side of the planet to get to the girl. On the way he manages to neurally link into a large flying creature that flies very fast, only to discover that it is intelligent and they soon become friends. When he gets to the girl she doesn't recognise him so he gets mad and starts attacking only to realise that it's all been a test set up by these people to allow him to reach higher levels of magic.   There were supposed to be sequels but I never got around to reading them.  I remember the cover art depicted a large dragon like creature with a torso of a man and a woman standing in front of it looking back at him.  Any idea what this book may be? Infinite Series $\sum\limits_{n=1}^\infty\left(\frac{H_n}n\right)^2$ How can I find a closed form for the following sum? $$\sum_{n=1}^{\infty}\left(\frac{H_n}{n}\right)^2$$ ($H_n=\sum_{k=1}^n\frac{1}{k}$). I'm going to install 64 bit 14.04 on a new machine with something like 1 to maybe 128GB RAM and even more RAM later. How much space should I allocate to the swap partition?   And especially: WHY those recommendations for these numbers?    (None of the existing answers  and  explain any of the why and are a bit dated if we look at 1GB or RAM and up) ravel: opposite meanings? Restore deleted photos I accidentally deleted the entire "downloaded" album full of pictures from my Samsung Galaxy S2 (SPH-D710) and am trying to use a  I downloaded.  My phone will not show up as a remove-able storage device on my computer, or on the program. I have tried to change the USB settings on my phone but there is no USB settings when I go to Settings > Wireless and networks as most information instructs.   I found the setting for USB debugging by going to Settings > Developer options and can turn that on and off, but that is the only setting I can find relating to USB storage.   When I connect it to the USB cord it gives me MTP or PTP options but again no USB options.   Any advice??? Thank you! Finding the derivative of $x\uparrow\uparrow n$ I am trying to find a general derivative for the function: $f(x)=x^{x^{x^{...^{x}}}}$however to do that I must find $f^{\prime }$ and $f^{\prime \prime}$...etc. I am now trying to write down a general expression for $f^{\prime \prime}$ and I have stumble opon the series in the picture below, I wonder, do anyone have an idea of what sort of expantion it migth be ? I have tried breaking it down into three different sums, but I wasn't very successful!  EDIT  So since this post has gotten some attention and the title has been change I will tell you what I am on about, although I already have a post just for the question in the title from before. I am as I said earlier trying to find a general derivative for the function $f(x)=x^{x^{x^{...^{x}}}}$ where $n$ is an arbitrary number, natural number and greater or equal to 2. I have already made success when I tried to find the first derivative, and I have also found some interesting pattern emerge when the derivatives as well as n incresses. But my question here was if anyone knew what this expation might be or look similar to be, since I have yet to be lernt series etc. I did not know that the question needed such background since it's straight a forward question. Is it possible to test apex that relies on field history tracking? I have some code that relies on field history tracking by querying the History for a custom object. This works fine, but it appears that the history records aren't created during the test so none of my tests will pass. Just noticed this:  Someone @replied to me in a question which appropriately showed up in my feed.  I go to click on that notice in the feed, and it presents me with "Loading the question failed."  I'd show a picture, but I don't think that it's entirely relevant - I believe it's reproducible if an answer is posted, someone makes a reply, the answer is removed, then that someone else goes back in the feed to try and revisit the post.  Alternatively, why not synchronize the interface between what a 10K user sees on the site, and what they see in the app?  As a 10K user, I would expect to see deleted questions and answers. Can matter really fall through an event horizon?