How to use sed to remove variables value from a string
How do I use variables in a sed command?
I´m not sure how to start with this proof, how can I do it? $$ \limsup ( a_n b_n ) \leqslant \limsup a_n \limsup b_n  $$ I also have to prove, if $ \lim a_n $ exists then: $$ \limsup ( a_n b_n  ) = \limsup a_n \limsup b_n  $$ Help please, it´s not a homework I want to learn. Words to describe people with good/poor vocabularies Words to describe people with good/poor vocabularies. I am looking for words which I can use to describe characters and I would also like to describe their vocabularies, and explain how their vocabularies stem from their upbringing Proof of "well-founded iff there is no sequence $x_n$ s.t. $(x_{n+1}, x_n) \in R$" I tried to do the following exercise from a book I'm reading, can you tell me if my solution is correct? Thanks!  Theorem 2: Let $R$ be a binary relation on a set $X$. Then $R$ is strictly well-founded iff there is no sequence $(x_n)_{n \in \mathbb N}$ of elements of $X$ such that $(x_{n+1}, x_n) \in R$ for all $n \in \mathbb N$.  Exercise:  (i) Formulate an analogue of Theorem 2 for  well-founded relations.   (ii) Prove Theorem 2.    (i) Theorem 2': Let $R$ be a binary relation on a set $X$. Then $R$ is well-founded iff there is no sequence $(x_n)_{n \in \mathbb N}$ of elements of $X$ such that $(x_{n+1}, x_n) \in R$ and $x_n \neq x_{n+1}$ for all $n \in \mathbb N$.  (ii)   $\implies$: Assume there is a sequence $x_n$ with $(x_{n+1},x_n) \in R$ for all $n \in \mathbb N$. Then the set $Y = \{x_n \mid n \in \mathbb N\}$ and hence $R$ is not well-founded since for every element $x_n$ there is $x_{n+1} \in Y$ with $(x_{n+1},x_n) \in R$.  $\Longleftarrow$: Let $R$ be strictly well-founded. Assume we have a sequence $x_n$ with $(x_{n+1},x_n) \in R$ for all $n \in \mathbb N$. Then by the same argument as above $R$ is not well-founded, hence there cannot be such a sequence.   I must be missing something but I can't seem to figure out what. Passing Account ID to my Visualforce Page As the user goes into an account, there is a custom button that they can click that will redirect them to my Visualforce page.  How can I capture that account id  in my controller?  Thanks  public myControllerCBR(){     breachRecord = new List&lt;wrapperClass&gt;();      AccountTeamMember uId = [SELECT UserId FROM AccountTeamMember WHERE AccountId =:ApexPages.CurrentPage().GetParameters().Get('id') and TeamMemberRole = 'Sales Engineer' limit 1];      List&lt;User&gt; uName = [SELECT Name, Manager__c, MANAGERID, Email, MOBILEPHONE FROM User WHERE Id =:uId.UserId limit 1];       for(User rept : uName){         breachRecord.add(new wrapperClass(rept));     }  }   See button setup: An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$ Are we inside a black hole? I was surprised to only recently notice that      An object of any density can be large enough to fall within its own   Schwarzschild radius.   Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's.  Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards.  Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light.  Or Mt. Everest packed into one nanometer.  Reading on about this , it increases proportionally with total mass.  Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.  Question: For an object the , what would have to be its diameter for it to qualify as a black hole (from an external point of view)?  Would this not imply by definition that:   The Earth, Solar system and Milky Way are conceivably inside this black hole? Black holes can be nested/be contained within larger ones? Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside? Why must we "avoid discussions in comments"? I've just started getting these messages:     Please avoid extended discussions in comments. Would you like to automatically move this discussion to chat?   Why should one avoid doing this? I think it adds to the site...  (Tagged  in more ways than one!) Disable display of passwords on an iPhone? Once you have defined a passcode to unlock an iPhone, and for every application asking a password, when waiting for a password an iPhone makes a transient display of any character you type. It is clear that this transient display was purposefully set in place to help people who have problems with passwords or with the on screen keyboard. This transient display lasts 3 seconds to avoid too big a security problem. But this is still largely sufficient for anyone behind you to read it really easily. Moreover this transient display can be easily captured by any camera or by a software on the iPhone:    I evaluate this echo of any password as a serious risk. This echo partially exposes a secret.  Is there any simple configuration method to suppress everywhere this mechanism of transient display of any password?    For information, I reported this security problem at :     Once I have defined a passcode to protect my iPhone, and within every   application asking me a password, when entering my password iOS makes   a transient display of any character I type. I guess that this   transient display of passwords was purposefully set in place to help   people who have problems with passwords or with the on screen   keyboard. This transient display lasts 3 seconds to avoid to create   too serious a security problem. But this is still amply sufficient for   anyone behind you to read it really easily.      This transient display can be easily captured by a camera   surreptitiously activated by a malicious neighbour.      I didin't find any easy way to block this security weakness with iOS 7   up to iOS 9.      How to disable this transient display of any password on iOS? How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$? I want to prove the following theorem (no idea whether it has a name):  Let $V = \mathbb{R}^n$ or $\mathbb{C}^n$ and $\|\cdot\|$ be a norm on $V$. Then, there exist $C_1, C_2 &gt; 0$ such that for all $x \in V$:  $$C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$$  I first let $x \neq 0$ (otherwise it would be trivial). Then, I divided by $\|x\|_\infty$ and normalized the vector $x$ such that $\|x\|_\infty = 1$. That left me with  $$C_1 \leq \|x\| \leq C_2$$  but I don't see how this could help me or how I could possibly limit an unknown norm. How can I proceed? Or is this the wrong way anyway? Thanks for any answers. Answers to a  mention that it is illegal for a US citizen to enter/leave their home country on a foreign passport. However this raises the following questions:   What is the maximum prescribed penalty for violating these rules? Are US immigration officials known for actually applying the penalty? E.g. the Cuba embargo banning visits to Cuba was almost never enforced, so it's possible this law is ignored as well. Java reading a file into an ArrayList? 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? Can you lose an ability if your reputation falls below a threshold? Why do I need an extended partition? What is an extended partition? Why do I need to use it to install Ubuntu if I already have four partitions that are factory installed? How to change launcher icon Is there a way to customize a Lucid Lynx Launcher icon for various programs? There does not seem to be a way to do this using Create Launcher or Launcher properties. The application is not actually "installed" on the PC, the executable has just been copied. All I've been able to do so far is to add the command /home/t32/bin/pc_linux/t32marm -c /home/t32/config_usb.t32 to a generic Launcher icon using Create Launcher. After upgrading to 12.04 from 10.04, can't login to PHPMYADMIN Grammar of "supposed to": part of speech / word class, active or passive? If I say     I'm supposed to go.   Is supposed to here an adjective in a passive construction? I was looking for proofs using Calculus for the area of a circle and come across this one $$\int 2 \pi r \, dr = 2\pi \frac {r^2}{2} = \pi r^2$$  and it struck me as being particularly easy. The only other proof I've seen was by a teacher and it involved integrating $x = \sqrt{r^2 - y^2}$ from $-1$ to $1$, using trig substitutions and then doubling the area to get $\pi r^2$ but the above proof seemed much more straight forward.  Is it a valid proof, or is it based on circular logic or some other kind of fallacy? How to enable MySQL client auto re-connect with MySQLdb? I came across PHP way of doing the trick:  my_bool reconnect = 1; mysql_options(&amp;mysql, MYSQL_OPT_RECONNECT, &amp;reconnect);   but no luck with MySQLdb (python-mysql).  Can anybody please give a clue? Thanks. How to check if a string starts with a specified string?