Countability of Different Sets
Cartesian Product of Two Countable Sets is Countable
Do these leaves signify anything? Occasionally, you can see little tufts of leaves blowing in spots on the map      Do these mean anything? When "etc." is at the end of a phrase, do you place a period after it? Example:     It's all about apples, oranges, bananas, etc.   VS.     It's all about apples, oranges, bananas, etc..   Update  What happens if the abbreviation is inside parentheses, do you place a dot after and before the closing parenthesis?     It's all about fruit (apples, bananas, etc.). How to display Trash and Home folder icons? Format timedelta to string Is every complex (smooth) manifold a scheme? The question in the title doesn't quite make sense. I was always wondering if the scheme is the generalization of manifold. The precise statement should be like following:  If $X$ is a complex (smooth)manifold, is there a scheme $Y$ over $\mathbb{C}$ such that the corresponding analytic space $Y^{an}$ isomorphic to $X$?  I guess if $X$ is projective, then this is Chow's theorem. And I doubt the question has an affirmative answer if $X$ is non-compact (I guess that $X: y-e^x=0$ in $\mathbb{C}^2$ might be an example, but I do not know how to show this).  Edit 1:  There are also example (as @hunter pointed out) of a complex torus but not an abelian variety shows that a compact manifold might not be a variety, however, is it possible to be a scheme ?(according to Hartshorne, the category of varieties is a subcategory of quasi-projective, integral, separated scheme. But could there be some non-quasiprojective scheme($Y$ has to be integral, separated in our case according to GAGA, I guess) )?  Edit 2: Another question I think of is: is (Artin) Stack a generalization of manifold? I really want to know if manifold could be think of some subcategory of some category of with "algebraic objects". How can I take a site offline using Drush? How to use itemize in Table environment I want to create a table like the picture below, and i wish to itemize the lamba_1 > lamba_2 > 0 using 'item style', which is the cell of each categories. Can someone help me? Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$? error: no such partition. Grub rescue How to show $(a^b)^c=a^{bc}$ for arbitrary cardinal numbers? One of the basic (and frequently used) properties of cardinal exponentiation is that $(a^b)^c=a^{bc}$.  What is the proof of this fact?  As Arturo pointed out in his comment, in computer science this is called . Mafia 3 no more damage to be dealt barclay mills Install a .NET windows service without InstallUtil.exe How do you fix a bad merge, and replay your good commits onto a fixed merge? I accidentally committed an unwanted file (filename.orig while resolving a merge) to my repository several commits ago, without me noticing it until now. I want to completely delete the file from the repository history.   Is it possible to rewrite the change history such that filename.orig was never added to the repository in the first place? Pumpkin Noodles is a thing or are a thing? Which of the following is correct?  How come pumpkin noodles is not a thing?  or  How come pumpkin noodles are not a thing?  I want to post one of the above statements to Twitter with a picture of a bowl of pumpkin noodles i.e. the stuff that comes out of a hollowed out pumpkin. Flames with no gravity? I was watching  today, and noticed this: in some moment the space station changed orbit and the people inside experienced zero-gravity. At that moment, a candlestick passed floating in the air, with the candles burning ().   But in our environment the flames go upward because the hot air is less dense, and that effect should disappear when no gravity is present, am I right? How would a candle flame look then? Change style properties of several layers simultaneously? I've read many years ago in books, that the brain has no nerves on it, and if someone was touching your brain, you couldn't feel a thing.  Just two days before now, I had a very bad migraine, due to a cold. It's become better now, but when I had it I felt my head was going to literally split in half, as the pain was literally coming from my brain.  So it lead me to the question: How come people can get headaches if the brain has no nerves? Plural or singular verb for collective term When to use a preceding slash in path names? (e.g. for the 'cd' command) I am a novice user and I am trying to install Oracle Java. The process calls for me to access /usr/local/java, but here is the problem. I get as far as /usr/local, then this is the message I get:  leonard@leonard-MT6452:/usr/local$ dir bin  etc  games  include  java  lib  man  sbin  share  src  leonard@leonard-MT6452:/usr/local$ cd /java/ bash: cd: /java/: No such file or directory  leonard@leonard-MT6452:/usr/local$ rm -r ~/java rm: cannot remove ‘/home/leonard/java’: No such file or directory   Help? How do you get the index of the current iteration of a foreach loop?