What are the disadvantages of setting every property to strong?
Differences between strong and weak in Objective-C
Combinatorial Proof I have trouble coming up with combinatorial proofs. How would you justify this equality?  $$ n\binom {n-1}{k-1} = k \binom nk $$ where $n$ is a positive integer and $k$ is an integer. Solving 4 Quadratic Simultaneous Equations Consider the equations:   $$\begin{cases} ab+c+d=3\\ bc+d+a=5\\ cd+a+b=2\\ da+c+b=6 \end{cases}$$   Where $a,b,c,d \in \mathbb{R}$. How can we find $a,b,c,d$?   The furthest I've got is by adding the first two equations and the last two equations together to get: $ab+bc+c+d+d+a=(b+1)(a+c)+2d=8$ and $(d+1)(a+c)+2b=8$ We can rearrange these (assuming $b,d \neq -1$) to get $$\frac{8-2d}{b+1}=\frac{8-2b}{d+1} \implies -d^{2}+3d+4=-b^{2}+3b+4$$ Which leads us further to $$b^{2}-d^{2}-3(b-d)=0 \implies (b-d)(b+d-3)=0$$ Now since $b=d$ gives us an absurdity (equations 1 and 4 reduce to 3=6), we must have $b+d=3$. This is as far as I can get unfortunately, since trying the same approach with the other pairs doesn't work in the same way.  Help would be much appreciated; the problem is from the BMO1 2004 paper. Ubuntu 18: Top bar for all monitors I just installed Ubuntu 18. Since the top bar is only on the primary monitor, I can't use the mouse to grab and move my Chrome window (the top of the screen looks like below). Trying to do so results in grabbing a single tab and opening it in a new window.     Is there a way around this? Ideally, I'd like to have the top bar  across all screens. Another obvious disadvantage of only having the top bar on one screen is that the window menu of any window, not just Chrome, is displayed on the left upper corner of my left screen even when the window is in the lower right corner of the right screen. Prove that for for all $p,q\in \mathbb{Z}$, $q&gt;0$ we have: $$ \left| \sqrt{2}-\frac{p}{q} \right| &gt; \frac{1}{3q^2}. $$  To be honest, I do not know where to start - any help would be appreciated. My Ubuntu version 18.04 brings me a GNU GRUB version 2.02 and I cannot access my entry password panel? How to add days to current Date using JavaScript. Does JavaScript have a built in function like .Net's AddDay? Good-morning Math Exchange (and good evening to some!)  I have a very basic question that is confusing me.   At school I was told that $\sqrt {a^2} = \pm a$  However, does this mean that $\sqrt {a^2} = +2$ *and*$-2$ or does it mean: $\sqrt {a^2} = +2$ *OR*$-2$  Is it wrong to say 'and'? What are the implications of choosing 'and'/'or'  Any help would be greatly appreciated. Thanks in advance and enjoy the rest of your day :) Changing an element's ID with jQuery I need to change an element's ID using jQuery.    Apparently these don't work:  jQuery(this).prev("li").attr("id")="newid" jQuery(this).prev("li")="newid"   I found out that I can make it happen with the following code:  jQuery(this).prev("li")show(function() {     this.id="newid"; });   But that doesn't seem right to me. There must be a better way, no? Also, in case there isn't, what other method can I use instead of show/hide or other effects? Obviously I don't want to show/hide or affect the element every time, just to change its ID.  (Yep, I'm a jQuery newbie.)  Edit I can't use classes in this case, I must use IDs. This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How do I start writing my first unit test?  How do I unit test this code?  I need help writing this unit test.   Salesforce Stack Exchange looks for detailed, specific questions that the community can help you with, and can't write tests on your behalf. We feel that working with the resources below can help you get started, and we encourage you to make an attempt to write your test and return to SFSE with your specific questions when you encounter challenges you can't resolve. In the DC Comics Universe, What Happens to Earthlings Under a Red Sun? I know in the earliest versions of Superman, his powers weren't from the yellow sun, but that was changed and, in general (at least as I understand it), Superman's powers are because he was native to a world with a red sun and now he's under a yellow sun.  What happens to an Earthling or other native to a yellow sun planet when near a red sun?  And what if the sun is blue?  Or a brown dwarf?  Please note: I'm asking about a red sun, not about living on Krypton.  Okay, that's heavy gravity, but it's not the only planet under a red sun.  (But, still the point about whether yellow sun natives would have super powers would come into play there, wouldn't it?) How to solve missing libmng.so.1 in Trusty (14.04) Package is no more available I would like to run SoulseekQT. However unfortunately one of the dependencies is libmng1, which is no more included in Trusty. sudo apt-get install libmng.so.1 or libmng1 or libmng1:i386 in Trusty (14.04) no more available. Do you have any idea how to solve this conflict? I mean is it really sure that libmng1 is excluded? Could I use libmng2 somehow instead? If not, could I somehow rebuild libmng1 for Trusty? Or do I have to downgrade back to Saucy (13.10)? Let $a$ and $b$ be positive reals. Show that $$\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$$ When to capitalize words such as "lake", and when can the whole word be omitted? Which of the following sentences are correct?     "He gave two examples of large lakes, Lake Michigan and Lake   Superior."      "He gave two examples of large lakes, Michigan and Superior."      "He gave two examples of large Lakes, Michigan and Superior."      "He gave two examples of large lakes, Lakes Michigan and Superior."   This question is primarily about what variants are formally correct, not which one sounds the best.  I think that the question should be valid for several words of the same kind, such as mountain (Mount), figure (Figure), table (Table) and so on. Prove $\lim_{x\to0}\sqrt{4-x}=2$ using the precise definition of limits. (Epsilon-Delta) How can I add a class to a block with code (development) For theming reasons I'd like to add a specific class at the "block" level to some of the blocks I'm generating with a custom module. I know there is a module , but I would rather like to do it directly in code (there is no need to change is afterwards).   I also know of , but that does not seem to allow adding or editing classes.  Is it possible to add a class with to a block from within my module code? I'm using Drupal 7. Electric Flux - What is the point? Electric flux is a defined quantity that is proportional to the no. of field lines passing through a given area element for a given electric field. It is not proportional to the relative density of field lines, which would supply information regarding the strength of the field at that point. Electric flux, it seems to me, does not supply us with any practical information. It seems to me that electric flux is a quantity defined and modeled specifically for Gauss' law, to introduce some kind of mathematical elegance to it and to introduce an additional visual aspect to the concept of electric fields. Perhaps this is why for symmetrical situations especially, Gauss' Law can be used to easily determine the electric field due to the given charge distribution. Am I wrong here? Is there a physical significance to electric flux that I do not understand? On freedom in Sartre's existentialism I am reading "Existenstialism is a humanism", the text of the famous conference by Sartre in which he explains his own version of existentialism. I think is full of logical inconsistencies, but maybe it's just because I don't understand it or I don't know enough about existentialism. Anyway, my question is about a specific passage. After having "demonstrated" that there is no way one can derive an ethics outside of Man (God does not exist and reason is insufficient), he asks himself according to what principle a person should behave and he says:     "For I declare that freedom, in respect of concrete circumstances, can   have no other end and aim but itself; and when once a man has seen   that values depend upon himself, in that state of forsakenness he can   will only one thing, and that is freedom as the foundation of all   values. That does not mean that he wills it in the abstract: it simply   means that the actions of men of good faith have, as their ultimate   significance, the quest of freedom itself as such."   So it seems Sartre says that when deciding a course of action, people will always choose "freedom," (and also, elsewhere, that "freedom" is always a good thing). That is for him the only principle, the only moral that governs or should (because we can do wrong judgments about what is freedom) govern our action.  My questions are:  1) do I understand correctly Sartre's thinking?  2) He says: a) freedom is absolute; b) the values that man chooses are also absolute because no God or reason can tell him what to do, c) therefore man will choose freedom. Is there any logic in this statement? If I replace freedom with X where X is "pleasure" or "justice" or "pain" or "zero temperature", wouldn't I "demonstrate" by this logic that man will choose X?  3) assuming what I said makes any sense, how can existentialism ever find a rule of moral conduct? and if it does, what is it and how can be demonstrated? and if it cannot, why is or has been important at all as a philosophy?  Thanks! Integrating MySQL with Python in Windows How to make existing public files private? Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$ I know how to prove the fact that $ p$ | ${ p \choose k } $ (when writing it as a fraction, $p$ cannot be divided by any of the $1\times2\times...\times k$ or $1\times2\times...\times(p-k)$ because $p$ is prime).  When I try to apply the same rationale for $ p$ | ${ p^n \choose k } $ I get stumped because $p^n$ is in fact divisible by one of the $k! = 1\times2\times...\times k$, where $0 &lt; k &lt; p^n$.  If we take the example of $2^3$ and $k = 7$, we can easily see that $k! = 1 \times 2 \times ... \times 6 \times 7$, and $2$ clearly divides $2^3$.  How else can I approach this?