Relationship between $\|\cdot\|_p$ and $\|\cdot\|_{\infty}$
"Scaled $L^p$ norm" and geometric mean
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros Difference between live and neutral wires In domestic electrical circuits, there are 3 wires - live, earth and neutral. What is the difference between the live and neutral wires?  As there is AC supply, it means that there are no fixed positive and negative terminals. Current rapidly switches direction. Does that not mean that both the live and neutral wires carry the same amount of current, alternatively? Why is the neutral wire called 'neutral'? Comparing $\pi^e$ and $e^\pi$ without calculating them Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$ $f(z)$ is a function such that $|f(z)| &gt; |z|$ for all $z\in\mathbb{C}$  How would you prove the function $\frac{1}{f(z)}$ is bounded. I think you have to use the $|f(z)|\leq M$ but I'm not sure. Delete all but top n from database table in SQL What's the best way to delete all rows from a table in sql but to keep n number of rows on the top? Connecting GSM SIM900A module with Ardunio I have bought an SIM900A Mini V4 GSM module. Here is the module,   I want to configure with arduino to send and receive SMS.   Do I have to connect TXD of this module--Tx of Arduino &amp; RXD of this module--Rx of Arduino or other way around?  There is no datasheet or documents on this new module.  When I search about RXD &amp; TXD, I found this in      TxD means "Data to be transmitted over the comms link" - which will clearly be an input to the modem;    Similarly, RxD means "Data that has been received from the comms link" - which will clearly be an output from the modem.    But I couldn't send or receive SMS using this configurations.  As I am new to this, It would be very helpful if anyone help on this.  Thank you in advance. I am looking for an example of a sequence which shows that, $a_{n+1} - a_n \to 0$ as $n \to \infty$ does not imply that sequence $a_n$ converges. I have a feeling that the sequence should be an oscillatory one but I am unable to think of an example. When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module? Assume that $M$ and $N$ are two finitely generated $R$-modules. Then $\operatorname{Hom}_{R}(M,N)$ is a finitely generated $\mathbb Z$-module and/or $R$-module (in this case, assume that $R$ is commutative)?   Note that $R$ is not Noetherian ring. Is there any counterexample (for any cases)? Are user accounts on data.stackexchange.com and Stack Exchange two different entities? I tried to search for similar questions, as I always do, but was not able to find one. I just created a new  on Data.Stack Exchange with my existing Google OpenID and it seems to be not associated with my regular Stack Exchange account. Is this by design? and if so, why? Identical creatures entering the battlefield How is the popularity of "recent tags" calculated? How are these calculated? I see them going up and down all the time, and there are obviously way more than 48 questions about C# so how are these calculated? Does the scientific community consider the Loschmidt paradox resolved? If so what is the resolution? Restrict the scope of a command to the execution of another command (java) ObjectInputStream deserializing wrong version of object This is a question from the free Harvard online abstract algebra .  I'm posting my solutions here to get some feedback on them.  For a fuller explanation, see  post.  This problem is from assignment $5$.     Prove directly that distinct cosets do not overlap.   Let $H$ be a subgroup of $G$ and let $a$, $b$, and $c$ be elements of $G$ such that $b\not\in aH$ and $c$ is in both $aH$ and $bH$.  Then there are elements $h$ and $h^\prime$ in $H$ such that $c=ah$ and $c=bh^\prime$.  So $ah=bh^\prime$ and $b=ahh^{\prime -1}$.  But $hh^{\prime -1}\in H$ so $b\in aH$.  This contradicts our original assumption. Therefore, there can be no element in more than one distinct coset.  Again, I welcome any critique of my reasoning and/or my style as well as alternative solutions to the problem.  Thanks. Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$ Sometimes I hear sentences that sound conditional to me, just because of the (unassertive) ordering of the words. I don't know if I can come up with a proper example. Consider this:          I'd be a lot better, had she stayed with me.        And I guess it's equivalent to this conditional form: If she had stayed with me, I would have been a lot better.  So, this is my question: In what ways can you make a sentence conditional without using conditional conjunctions (if, unless, etc)? And what are their equivalent conditional forms? Gandalf (as with all the Istari) did not have a corporeal form before coming to Middle-earth and was essentially ageless. We also know that Gandalf did age, albeit very slowly, while on Middle Earth. By the end of the Third Age (before battling Durin's Bane), he had the appearance of an old human male (non-Númenórean, etc) in his 70's or 80's. This leads me to wonder:  Is there any indication in Tolkien's writings that describes Gandalf's appearance (in human-looking years) when he arrived in Middle Earth? In other words, was Gandalf the Grey originally "Gandalf the Tall Dark &amp; Handsome in his 20's"?  I'm not talking about his actual age, but rather his appearance in human years. How do I know the script file name in a Bash script? How can I determine the name of the Bash script file inside the script itself?  Like if my script is in file runme.sh, then how would I make it to display "You are running runme.sh" message without hardcoding that? Duplicate:                      The number of residents has grown.    The number of residents have grown.      Which of the above sentences is grammatical? Since has should stick with singular nouns and have with plural ones, I guess (2) should be correct, but I'm not sure.