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Completeness and Incompleteness It would be nice to  for .  As it is, SE kind of stands out (in a not cool way): Prove that a set in $\mathbb R^3$ is not an algebraic set I want to prove that the set $\{(\cos(t),\sin(t),t)\in A^3(\mathbb R); t\in \mathbb R \}$ is not an algebraic set.   I already proved that the set $\{(\sin(t),t)\in A^2(\mathbb R);t\in \mathbb R \}$ is not algebraic but the method that I used doesn't seems to be general. If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$ Did not find this from this website...  If $$ \gcd(a,b)=1,$$ then there exists integers $x$ and $y$ such that $$xa+yb=1.$$  Now, the tip is to use particular corollary, that states:  The class $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}\Leftrightarrow \gcd(m,n)=1.$  I am totally lost with the corollary.  Let's assume that $\gcd(m,n)=1$. Then, $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}$.  OK! Then what?  There is also follow up, where I have to prove the converse. I am familiar with Bezout's lemma. I was able to read and write NTFS filesystems normally in Mountain Lion, but after the upgrade this stopped to work.  I installed ntfs-3g and fuse4x using homebrew in Mountain Lion and followed the instructions displayed by homebrew to finish the installation of fuse4x kernel extension.  To try to solve this problem I removed ntfs-3g, fuse4x and fuse4x-kext and reinstalled them. But this didn't solve my problem.  Does anyone know how to solve this? Thanks. What do the plus and minus signs mean in Objective-C next to a method? Consider this conversation:      John: I am giving free chess lessons.   Mary: Nice! You’re a true teacher.   John: How so?   Mary: A true teacher imparts knowledge without a price tag.   John: But what if teaching is his only source of income? Would he not be a “true” teacher then?   Mark (in response to the question above): You clearly mentioned “free chess lesson”.   I don’t see how Mark’s comment adds anything to the discussion or makes sense in the current discussion. It is “redundant” — that’s one word for it — but is there a more fitting word? I have six upvotes for the one question with no intervening history. They have been summarised into two groups - one with 4 events and one with 2 events. However, when you expand either, both show all 6 events. Minor I know, just letting you know. Let $X$ be an arbitrary random variable  takes values in $\{0,1,2,...,10\}$. What are the minimum and  maximum values of variance of random variable $X$? After T-2, why not send back another T-800? Can I mix MySQL APIs in PHP? How do I complete "Find the Bitizen"? In tiny Death Star, Palpatine has given me the mission "Find the Bitizen" with the text "Working for tips is acceptable. Find 1 Bitizen(s)."  I assumed I had to wait for one of the events where you have to find a "rebel scum" and tap on it to get rid of. One of those events finally popped up but it did not complete the mission.   How do I complete this mission? What level is a spell if you cast it without expending a spell slot? There are ways to cast spells without expending a spell slot such as:  Master Transmuter (PHB 119):     Restore Life. You cast the raise dead spell on a creature you touch   with the transmuter’s stone, without expending a spell slot or needing   to have the spell in your spellbook.   Armor of Shadows (PHB 110):     You can cast mage armor on yourself at will, without expending a spell slot or material components.   Whispers of the Grave (PHB 111):     You can cast speak with dead at will, without expending a spell   slot.   See also: Channel Divinity: Read Thoughts (PHB 59-60), Mystic Arcanum (PHB 108), Beast Speech (PHB 110), Chains of Carceri (PHB 110), Eldritch Sight (PHB 110), Fiendish Vigor (PHB 111), Mask of Many Faces (PHB 111), Master of Myriad Forms (PHB 111), Misty Visions (PHB 111), Otherwordly Leap (PHB 111), Signature Spells (PHB 115), Spell Mastery (PHB 115), Shapechanger (PHB 119), Boon of Spell Mastery (DMG 232) and Boon of Spell Recall (DMG 232).  What level are these spells if you cast them without expending a spell slot? Fantasy/scifi combo - band of travelers who must get from "sphere" or domain to domain - each geographic area is ruled by a magician - it turns out later these are people who are unwittingly tapping into the computer grid they all live on to alter their own reality? Bit error rate calculation for LIN protocol I am having this microcontroller -   I am using an 8MHz external clock. I want to calculate the Bit error rate of my LIN Communication. My LIN Communication Baud rate is 19.2kbps. My questions :  Can I use the LPUART Module in the Mirocontroller for the LIN Communication?  How to find the Bit error rate for the LIN Protocol communication for my baud rate of 19.2kbps and external clock of 8MHz.   I found this below from the reference manual. But not sure, how to calculate the Bit error rate from this.   How to calculate the SBR Register value, OSR and the LPUART ASYNCH Module clock?  Please help 3 input XNOR gate operation "It's cold today" -- what term do linguists use to call "it" when it's used as the subject of a sentence, but has no real antecedent? Ubuntu 18.04 bond with netplan duplicate MAC address after cloning "strlen(s1) - strlen(s2)" is never less than zero Would you please explain the difference between these two sentences?     Spain ceded (or gave) Puerto Rico to the United States. Since then, Puerto Rico has been a U.S. territory.      Spain ceded(or gave) Puerto Rico to the United States. Since then, Puerto Rico was a U.S. territory.   I am stuck between 'has been' and 'was' in the above sentences.