Defining custom commands with output dependent on the number of variables
creating a diagonal matrix with a variable amount of parameters
What does the human body use oxygen for besides the final electron acceptor in the electron transport chain? My biology teachers never explained why animals need to breathe oxygen, just that we organisms die if we don't get oxygen for too long. Maybe one of them happened to mention that its used to make ATP. Now in my AP Biology class we finally learned the specifics of how oxygen is used in the  due to its high electronegativity. But I assume this probably isn't the only reason we need oxygen.   What other purposes does the oxygen we take in through respiration serve? Does oxygen deprivation result in death just due to the halting of ATP production, or is there some other reason as well? What percentage of the oxygen we take in through respiration is expelled later through the breath as carbon dioxide? If neutrinos are disfavoured as DM candidates why aren't axions? I recently printed a paper that asks to prove the "amazing" claim that for all $a_1,a_2,\dots$  $$\sum_{k=1}^\infty\frac{a_1a_2\cdots a_{k-1}}{(x+a_1)\cdots(x+a_k)}=\frac{1}{x}$$  and thus (probably) that  $$\zeta(3)=\frac{5}{2}\sum_{n=1}^\infty {2n\choose n}^{-1}\frac{(-1)^{n-1}}{n^3}$$  Since the paper gives no information on $a_n$, should it be possible to prove that the relation holds for any "context-reasonable" $a_1$? For example, letting $a_n=1$ gives  $$\sum_{k=1}^\infty\frac{1}{(x+1)^k}=\frac{1}{x}$$  which is true.  The article is Prove that if $A$ is transitive, then $\mathcal{P}(A)$ is transitive too. My book on set theory says     Prove that is a set $A$ is transitive, then $\mathcal{P}(A)$ is also transitive, where $\mathcal{P}(A)$ is the power set of $A$.   I don't know understand how. Let $A=\{a,b\}$. Clearly it is transitive. Now $\mathcal{P}(A)=\{\{a\},\{b\},\{a,b\},\emptyset\}$. This is clearly not transitive. I’m not sure What it is? I’m trying to get a glossy shade to building in my scene as soon as I put roughness to zero I see these trees in glass. I have no trees in my scene anywhere, background is black. Even when I render I see these trees. How can I get rid of them and still keep my glossy building material. Why does the zoom sometimes stop at a point? I often find that I can zoom in to a point, but then cannot zoom any more, even when there is a lot of room to zoom to the meshes on the scene.   This is particularly annoying in the following scenario:  I often land up left clicking on the scene and the 3D cursor shifts there. I use Shift+C to shift the 3D cursor back to the origin. However, this also centers the view on the cursor and shifts the view to show all objects, and sometimes this zooms things way out &ndash; at this point, if I try to zoom in, I can zoom in to a point (using the pinch/zoom on trackpad), but then it stops zooming in.   How do I zoom in after that? Is there anything else I am doing wrong in this case? Another indicator of a review audit: Question has no tags What would happen to a teaspoon of neutron star material if released on Earth? I've read on NASA's page on neutron star that one teaspoonful of that star would weigh over 20 billion tonnes on Earth. If it was somehow possible to bring it to earth would it:   Burn and disappear during Earth atmosphere entry? Assuming we have 20 billion tonnes of mass occupying the volume of a teaspoon here on Earth, would it fall through the ground under its own weight? I don't understand why the interior of $\mathbb{Q}$ in $\mathbb{R}$ is empty, since, for every ball with the center being a rational number, given an $\epsilon&gt;0$, I can find an infinite sequence of rational numbers that approach this point. For example, take $\frac{1}{2}$. The sequence $\frac{1}{2}+\frac{1}{n}$ can be made as close as I want to the number $\frac{1}{2}$, therefore I can always have open balls with center $\frac{1}{2}$ such that there are rationals inside it. Is there a word or phrase for someone who works hard at night and does not sleep? All the words or phrases I know for people who stay up at night merely describe the habit of not sleeping (e.g.: a night owl or insomniac)  I am looking for a word or phrase with an emphasis on working hard at night. These people work are different from insomniacs because they have no problem sleeping but they refuse sleep to work. They are different from night owl because they wake up early in the morning.  To give more context, suppose a nurse with kids who has a normal day life like most people and takes care of the kids but also works most nights in a hospital. he or she vs their when using 'one' as a pronoun Mindfulness allows one to cope with their daily challenges.   Is "one" correct with "their" here?  I want to know if it is okay to user their (instead of he or she) when using 'one' as a pronoun. Is there a terminal command that will log you out of your current desktop session and take you back to the login screen? If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$ Cardinality of the set of all real functions of real variable How does one compute the cardinality of the set of functions $f:\mathbb{R} \to \mathbb{R}$ (not necessarily continuous)? I was going through the topic "formation of comparative and superlative".       The rule says     When two objects are compared with each other, the latter term of comparison must exclude the former, as in "Iron is more useful than any other metal". If we say "Iron is more useful than any metal", that is the same thing as saying    "Iron is more useful than iron", since iron is itself a metal.   I am finding difficulty to relate the rule with example. The boundary of union is the union of boundaries when the sets have disjoint closures Do $T$-invariant subspaces necessarily have a $T$-invariant complement? How can I solve this quantum mechanical "paradox"? I was trying to experiment with docker, Ubuntu 14.04, 64-bit. I managed to run an image, and I gave it the path on one of my removable drives, /media/Drive1.  Now, whenever I reboot, I see there is a /media/Drive1 with only a docker directory inside it, and the actual drive which should be Drive1 ends up mounted on /media/Drive11, and this happens every reboot - even when I unmount these drives, and do a sudo rm -rfv /media/Drive1 before rebooting!  So something probably creates /media/Drive1 before it is fully mounted, and I guess that something is docker, because when I boot, I have:  $ ps axf | grep docker  2085 ?        Ssl    0:00 /usr/bin/docker -d   So, how can I disable the docker autostart, so it doesn't interfere with the mounting of external USB drives at boot? Default constructor with empty brackets Is there any good reason that an empty set of round brackets (parentheses) isn't valid for calling the default constructor in C++?  MyObject  object;  // ok - default ctor MyObject  object(blah); // ok  MyObject  object();  // error   I seem to type "()" automatically everytime. Is there a good reason this isn't allowed?