I read in the book 'One two three infinity' by George Gamow that the cardinality of sets of all plane curves is greater than the number of real numbers and so it can be thought of as a strictly larger infinite crdinality $\aleph_2$. I wanted to know the reasoning or proof of this.
I am reading George Gamow's book  and a certain assertion Gamow makes seems a little startling considering what I already know of the subject of infinite cardinality.     But the number of all geometrical points, though larger than the number of integer and fractional numbers, is not the largest one known to mathematicians. In fact it was found the variety of all possible curves, including those of the most unusual shapes, has a larger membership than the collection of all geometric points, and thus has to be described by the third number in the infinite sequence. [Gamow, 22]   He later does explicitly say the number of all possible curves is $\aleph_2$. But nowhere else can I find reference to this being true, nor does he provide any sort of reasoning to its validity.  My question is how can you prove the set of all possible curves is of cardinality $\aleph_2$ and not $\aleph_1$ or $\aleph_0$?
I recently flagged a question as "very low quality", just like I've flagged many questions in the past. However, my flag was found to be unhelpful this time. The same thing happened when I recently flagged a post as not an answer.  Are the moderators being more strict when it comes to handling quality related flags? If so, why? Migrated question's answers can be upvoted twice by the same user was created on Server Fault, answered on Server Fault, I upvoted some of those answers on Server Fault, and then moved by consensus to Super User.  Now that the question is on Super User, I can upvote the same answers I previously upvoted on Server Fault. Which Ubuntu repositories are totally safe and free from malware? Normally to remove files with spaces in their filename you would have to run:  $ rm "file name"   but if I want to remove multiple files, e.g.:  $ find . -name "*.txt" | xargs rm   This will not delete files with spaces in them. How do I overload the square-bracket operator in C#? 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I have a scenario where I have multiple threads adding to a queue and multiple threads reading from the same queue. If the queue reaches a specific size all threads that are filling the queue will be blocked on add until an item is removed from the queue.  The solution below is what I am using right now and my question is: How can this be improved?  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Pages documents created on Yosemite cannot be opened by Pages on Yosemite after latest update (5.5.2) Seemingly every single document that I created in the previous version of Pages (I update regularly whenever I see that a new update is available) on this same MacBook Pro with Yosemite will now not open with Pages after the latest update (5.5.2). I am still on Yosemite and nothing has changed aside from updating Pages, Numbers &amp; Keynote.  All of my documents are stored on my internal hard drive. When I attempt to open them I get a message stating the following:     This document can't be opened because it's too old. To open it, save it with Pages '09 first.   As I mentioned above, however, these documents were created in whichever version was right before the current version on the same computer with the same operating system (Yosemite).  Can anybody help? These are time sensitive documents. For now, I may try opening them with my iPad, but wow, if I knew this was going to happen I certainly would not have updated. How to specifically use ntfsundelete to recover directory This is a followup on my original post  which may be deleted in the future.  In the process of backing up my audio books, I "permanently" removed a folder (with subfolders) that I had already exclusively moved to that drive. It's path is /media/gratis/Seagate Expansion Drive/Audiobooks/Jason Dark. The sole folder in that should be called John Sinclair; but I'm not sure about that.  Which tool offers the best chances to recover those files? I haven't written plenty on that drive afterwards; so I hope for the best. It's not that other methods failed; I just cant get my head around what to do and I want to be cautious. It's a NTFS Drive.  According to testdisk it has an "EFI GPT" Partition table.  Disk /dev/sdb - 5000 GB / 4657 GiB - CHS 608001 255 63, sector size=512 - Seagate Expansion Desk, FW:9401   Information According to "Disks" (Ubuntu Standard Software):  NTFS; GUID Partition Table; [...] Partition Type: Microsoft Reserved   Attempt 1: First off, ntfsprogs seems to no longer be in repos (those mentioned by another user); but it is already installed on my machine so no problems there. I always get the error:     Access is denied because the NTFS volume is already exclusively opened. The volume may be already mounted, or another software may use it which could be identified for example by the help of the 'fuser' command. You can use force option to avoid this check, but this is not recommended and may lead to data corruption.   Although I only just plugged it in and even quit Nautilus by force (nautilus -q).   Therefore, I ran sudo ntfsundelete /dev/sdb2 -f. That gave me a list of a bunch of files, 205013 to be exact. Now, what I want is the content of the directory .../Audiobooks/Jason\ Dark/ to be restored. What do I have to do? It's contents are .m4b &amp; .opus files and folders, of course. Is there a problem with the ClearBits data dump? How to run a server on port 80 as a normal user on Linux? I have Googled about a solution for quite some time, but couldn't find an answer.   I am on Ubuntu Linux and want to run a server on port 80, but due to security mechanism of Ubuntu, I get the following error:      java.net.BindException: Permission denied:80   I think it should be simple enough to either disable this security mechanism so that port 80 is available to all users or to assign required privileges to the current user to access port 80. Implement numbering scheme like A,B,C... AA,AB,... AAA..., similar to converting a number to radix26 I want to implement numbering scheme like Microsoft Word uses for numbering.  first one gets = A,next is  B, next is C, .... then AA, then AB,....and so on.  as shown below   A        B  C  .   .  AA  AB  AC  .  .  AAA  AAB  ....   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