Why is the naive notion of a product ideal not necessarily additively closed?
Defining the Product of Ideals
Show the post's comments on the "Suggested Edits" review interface Show that the series $\sum\limits_{n=2}^{\infty} \frac {(n^3+1)^{1/3}-n}{\log n}$ converges Show that the series $$\sum\limits_{n=2}^{\infty} \frac {(n^3+1)^{1/3}-n}{\log n}$$ converges.   I showed it using Abel's theorem and limit comparison test. Any other simpler method? How can I prevent my mail from being classified as spam? There is some behavior I can't understand in the Unity Desktop.   Open nautilus via. clicking in the launcher onto the home-button Navigate to for example the windows-partition in nautilus Minimize nautilus Click on nautilus in the launcher doesn't open the nautilus with windows-partition, instead it opens a new window with the home folder.   Is there a workaround for this strange behavior?  Regards, Arthur How is a second measured? And why is it measured that way? The earth's rotation around itself (one rotation around Earth's own axis) doesn't take exactly 24 hours. It off by some seconds which becomes somewhere around 6 hours per year and 1 day in 4 years(leap year), which brings the question why didn't we modify the measurement of 1 second ever so slightly so as to avoid leap years altogether.   Well how is 1 second measured exactly?  says      the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. []   Well, why is it measured that way? Is there any technical reason like it is easy to measure and can be standardized easily? Or is it really possible to modify the measurement of time? How to pack the game files into one without using any file compressor? Well, one example is this file of the game The Sims 2 for PS2: quickdat.arc. The file contains this .arc extension, but it's no one an archive file and it contains some data of the game inside. How can I do this? Put so many files in one?  How to do something like this? All the game files inside one without using a file compressor? SSD drives lifetime Some years ago when I was looking to buy an SSD drive, I remember reading about how SSD drives had low lifetime with frequent read/writes, so I backed off.  Now I see this in Specifications:  MTTF: 1,000,000 Hrs    That's 114 years (ok, it could be a few years less, but still WOW)    What has changed since then? What is your personal experience about this technology? Simple past or present perfect? Which is preferable, simple past or present perfect, in situations like this one: I had a conversation with my friend and we planned to do something; shortly afterwards I call him back to announce the accomplishments. My biggest doubt about simple past is that perfect aspect is used to indicate past action (accomplishment) with current relevance, at the same time I'm not sure if I'm allowed to use present perfect, because there's a gap between accomplishing and the current moment, which is a characteristic of simple past. Is there a difference between Bayesian and Classical sufficiency? The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent?  If there is a difference, what is it? Can you use Wish to duplicate a spell at a higher level? Wish allows you to duplicate the effects of any spell L8 or lower. Does that include a lower-level spell, cast at L8? Say, as a Wizard, casting Heal at L8.  I'm leaning towards yes, but it wouldn't be the first time I assume the wrong answer... $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $ = -$  2.887270... $  The function has no antiderivate and there's no symmetry here to help, if you solve this I would be thankful if you would for a highschooler ^^ Could we send a man safely to the Moon in a rocket without knowledge of general relativity? Eigenvalues and power of a matrix Problem installing .deb in Software Install Ubuntu 20.04 How do I add myself back as a sudo user? I clean-installed Ubuntu 11.10 today, and then installed VirtualBox.  This required me to add myself to the vboxusers group, and since 11.10 seems to no longer have a graphical app to add users to a group, I ran the following command:  sudo usermod -G vboxusers stephane   This is a problem.  I now see what I should have run instead is:  sudo usermod -aG vboxusers stephane   The end result is I'm no longer in the groups I should be in.  Including whatever group is required to run "sudo".  When I run any command as sudo now, I get the following:  $ sudo ls [sudo] password for stephane:  stephane is not in the sudoers file.  This incident will be reported.   Is there a way to fix this, or do I need to re-install from scratch again? I'm trying to install Linux alongside my 64-bit Windows 8 and went into my partition manager to find this structure.    In order to create partitions for my Linux install I need to free up some space. I see that the last partition is an empty recovery partition, as you can see highlighted, it's 100% free.  I was wondering is it okay to just remove this partition seeing as it doesn't appear I'll be losing anything?  Not sure if this helps but this is on a Fujitsu AH532 running Windows 8 64-bit with UEFI. I have added an mp3 file as a static resource, can someone please help me to call that resource in the lightning component so when I hit the button it will play that static resource  as per the Salesforce documentation I have tried below but instead of playing the sound it is displaying the message. If $E$ has measure zero, then does $E^2$ have measure zero? Currently I'm just working through measure theory just to see if its something I would like to take.  Unfortunately I am stuck on this problem from Carothers.     If $m^*(E)=0$, then $m^*(E^2)=0$.   Where $m^*$ denotes outer measure and $$E^2=\{x^2:x\in E\}.$$  I toyed with the idea that $I_k &lt; 1 \Rightarrow I^2_k &lt; I_k$.  However I am at a loss as to how to set up a chain of inequalities (which is what I am assuming I need). $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral Tracker icon is misaligned in activity page