Where is my error? A system is simply inconsistent is every formula is provable (if $\text{A} \wedge\neg \text{A}$ were provable for some formula $\text{A}$, then by $\neg$-introduction, any formula can be proven).  Taking the contraposition, we get that if there exist some formula that is unprovable, the system is simply consistent. Since the Continuum Hypothesis is undecidable and thus unprovable in $\text{ZFC}$, shouldn't that mean that $\text{ZFC}$ is simply consistent?  This also shows the other direction of Gödel's first theorem: if the system is incomplete, then it is consistent. I know all of this can't be right because I haven't read any of this and it can't be that easy, so I must be missing something.
I've read before that, by the Principle of Explosion, if a theory is inconsistent, then absolutely any statement can be proven within it.  Obviously, there are statements which are independent of ZFC (Continuum Hypothesis, etc). It seems to me that this proves that ZFC is incomplete. Why does it not then follow that ZFC is consistent? It seems to me that we could say "Assume ZFC is inconsistent. Then the the Continuum Hypothesis is provable in ZFC. But the Continuum Hypothesis is neither provable nor disprovable in ZFC. Therefore ZFC is consistent."  What am I missing here?
This has just dawned on me that if you're writing an operating system then what are you writing it on? I ask this as I am reading a microprocessor fundamentals book from 1980 and this question popped in to my head:   How was the first microprocessor chip programmed?  The answer may be obvious but its bugging me. I have an independent variable called "quality"; this variable has 3 modalities of response (bad quality; medium quality; high quality). I want to introduce this independent variable into my multiple linear regression. When I have a binary independent variable (dummy variable, I can code 0 / 1) it is easy to introduce it into a multiple linear regression model.  But with 3 modalities of response, I have tried to code this variable like this :  Bad quality      Medium quality      High quality       0                1                  0      1                0                  0      0                0                  1      0                1                  0   But there is a problem when I try to do my multiple linear regression: the modality Medium quality gives me NA:    Coefficients: (1 not defined because of singularities)    How can I code this variable "quality" with 3 modalities? Do I have to create a variable as a factor (factor in R) but then can I introduce this factor in a multiple linear regression? Is it two-third or two-thirds? Is it two-third or two-thirds? If both are correct, how does their usage differ? Give read-only access to specific folders? Possible Duplicate:          On  it's a stated fact that if $I$ and $J$ are coprime ideals of a ring $A$, then $I^k$ and $J^\ell$ are also coprime for any integers $k,\ell$.   There's no proof given. Why is this fact true? What are these dark spots in my pictures? I've been seeing these dark spots in my pictures. They appear a lot more on some pictures than others, but they are in the same place in the image and independent of the lens being used. Is this dust? I've also heard that you can get oil spots on the sensor.  The image is from a Nikon D7000. I have 4GB RAM. When I open Firefox, IntelliJ IDEA or VS Code and some other application my memory is about used up thus my machine hangs and I can't do anything. I can't even close any applications.    Date and time are shown in the top bar so that I can view it any time without any thing typing.   If I would view memory status in this way without typing anything then I can make a decision whether to open an application or whether this application may put my machine in hanging state or not.    Is it possible in Ubuntu 18.04 LTS? I have a USB drive that I can see/access/modify/etc in Linux/Ubuntu but it doesn't show up on my Mac OSX.  I did sudo fdisk /dev/sdb (where my USB is) and then g to create a new GPT partition table, n to make a new partition, used all default settings, then w to save and exit.  Then I did sudo mkfs.fat -F32 /dev/sdb1 to format the partition with a FAT32 filesystem.  I ejected the USB and put it in my Mac and it doesn't show up / get detected.  What did I miss? Line of Bones to Travel and Conform to Curve (Train or snake following path) Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$ It is given that $X,Y \overset{\text{i.i.d.}}{\sim} N(0,1)$  Show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}} \overset{\text{i.i.d.}}{\sim} N(0,\frac{1}{4})$  I was thinking of making polar transformations $X=r \cos \theta, Y=r \sin \theta$  Then I am getting stuck at ranges of $\theta$ Login screen resolution So I just installed Ubuntu 16.04 on my Dell XPS 13. When I get to the login screen it starts at 3200x1800 for a quick second, then I get a way lower resolution like 800x600 but as soon as I login it adjusts to 3200x1800. How would I get 3200x1800 permanently on my login screen? I didn't have this issue on 14.04. How does friction stop a car? Will my device work with Ubuntu? Deserializing JSON when sometimes array and sometimes object Temporary locks on answers not showing lock duration Tested on Stack Overflow, Stack Overflow Meta and Pets.  Questions  Temporary locks on questions are showing the duration (mod only).  Stack Overflow.   Meta Stack Overflow.   Pets.   Answers  On answers they are not and there's no way to find the lock duration when we use timeline tools to examine the post.  Pets.   Stack Overflow.   Meta Stack Overflow.   Is this something that hasn't been implemented or is it a bug?  If it hasn't been implemented can we please have it implemented? No output from goroutine extract string between double quotes I have requirement that i need to extract string using quotes. My string as follows.  "abcd efgh" "ijkl mnop" "qrst uvwxyz"   can you help me to get the string between second double quotes(ijkl mnop) using sed or grep command.  In other words if I say give me the string in first quotes I want the  first string; if I say second string it should give me string between second double quotes and similarly third one also. I want to write an application that detects when a page is loaded in the browser, then I should be able to insert content on top of the loaded web page? Anybody with an idea on how to do that?  Please note that I should be able to do this in any browser (Firefox/IE).  What language should I use to help me do this?  How do I detect this from an external application?  How should I integrate this with the browser? Accidentally hit "toggle full screen", How do I exit? I'm stuck in full screen in the node editor. Escape isn't working, and I have no menus and no idea how to leave except to quit Blender and reopen the program. I've just been downvoted. How should I react?