When I am looking at a question, which I could possibly have a solution but I don't understand the question properly.I try to ask more questions but I am not able to comment as I don't have have 50 rep points and I have to answer the questions, which means it gets down voted or flagged. This is really annoying. Why do we need 50 rep points, just to comment?
Users with less than 50 reputation points cannot write comments on questions and answers that they don't own.  Why does this limit exist? But I want to contribute now. What should I do instead? But I can't write a good answer without more information! Shouldn't I be allowed to post comments if I have reputation on a different site? But I saw a new user posting a comment! How did they do it? Why do I need 50 reputation to comment on my own post?   See also:    in the Help Center
Hyphen or no hyphen when modifying an adjective with a quantity? I have a sentence which has an object that is described with an adjective:     We need to inform our interested patrons of this change.   If I modify "interested" with "more" or "less", do I connect the words with a hyphen or not?  Example sentence:     We need to inform our less-interested patrons of this change.     Also, please let me know if I have not used the correct terms for sentence parts in this question. php/mysql with multiple queries Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists I have to show that set of all $x$ such that $x \in P$ and $x \notin Q$ exists. So, I think I have to assume that sets $P$ and $Q$ already exist. So, with that, I can use  . This axiom is $$ \forall w_1,\cdots, w_n \, \forall A \,\exists B \,\forall x \left( x \in B \Longleftrightarrow [ x \in A \wedge \varphi(x,w_1, \cdots , w_n, A)] \right) $$ So, I will let $\varphi(x, Q, P) = x \in P \text{ and } x \notin Q $. Also, I will let $A = P$ and  $w_1 = Q $. So using universal instantiation, I get the following $$ \exists B \,\forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge \varphi(x, Q, P)] \right) $$ And using, existential instantiation, there exists a set $B$ such that $$ \forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge \varphi(x, Q, P)] \right) $$ Using the definition of $\varphi(x, Q, P)$, this can be simplified as following $$ \forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge x \in P \wedge x \notin Q] \right) $$ $$ \forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge x \notin Q] \right)$$ $$ \forall x \left( x \in B \Longleftrightarrow x \in \{ x \,| x \in P \text{ and } x \notin Q \} \right)$$ Now, using , it will follow that $$ B = \{ x \,| x \in P \text{ and } x \notin Q \}  $$ And, since $B$ exists, this means that $\{ x \,| x \in P \text{ and } x \notin Q \} $ also exists. Is the proof good ? lstlisting - line number gaps Say I have two Chrome windows open like this:   It seems that the most recently used window always appears on top. In other words, the &quot;Apply Digital Signatures&quot; was the window I had open last. If I were to switch to the window showing the new tab, then the order in which the windows are displayed in the task bar suddenly changes. Is there a way to keep them from shuffling around? I'd like to be able to order them however I want, like tabs in a web browser. (I'd also like to put them across different workspaces.) Is there a way to recover deleted data from a SSD / USB Flash drive?  All I could find were recovery for damaged drives, but I want to recover deleted data.  So how do I do this? I am struggling to understand this. According to truth tables, if $P$ is false, it doesn't matter whether $Q$ is true or not: Either way, $P \implies Q$ is true.  Usually when I see examples of this people make up some crazy premise for $P$ as a way of showing that $Q$ can be true or false when $P$ is something outrageous and obviously untrue, such as "If the moon is made of bacon-wrapped apple-monkey carburetors, then I am a better wakeborder than Gauss."  $P$ is clearly false, but $P \implies Q$ is true no matter what the state of $Q$ is, and I don't understand why.  Are we saying "If $P$ is false, then all bets are off and $Q$ can be anything, either true or false, and not contradict our earlier claim, and if it isn't false, it must be true"?  Otherwise why can't we say that if $P$ is false, then we can't make any claims one way or the other on whether or not it implies anything at all? Repeating determiners: “the X and (the) Y” I have a problem with the use of "the" after "and" where you would basically be connecting words. For example, which of the following is better:     The table and the chairs?   The table and chairs?   Or are both okay? What is the rule, and are there exceptions to it? Or is the rule just contextual and may vary between the sentences and meanings? Reading grep patterns from a file The space $ C^1[0,1] $- the space of all continuously differentiable functions on $ [0,1]$ is not a Banach space with respect to the sup norm,$ \|.\|_{\infty} $ since the uniform limit of a continuously differentiable function need not be differentiable.  How can I illustate this statement using a counter example? Can I use $ f_{n}=\frac1 n \sin nx $ as a counter example?  Also, is $ C^1[0,1] $ is same as the space given by $ X=\{f\in C^1[0,1]:f(0)=0 \}$. Can I use the same example to show that this is not a Banach space?  More help is appreciated! Thanks! After having read various articles on this site about WWW or Non-WWW website setup, ,  and , and after having setup a correct redirection rule in .Htaccess to at least eliminate duplicate contents (currently the non-www solution (e.g. http://example.com) I have a feeling that my site rank less since I changed this.   My confusion was strengthened by these two opponents:     &amp;     Could the change of www.example.com >> http://example.com have a factual impact on ranking?  say either is better or worse. Are they holding information back?  I am confused fellow folks...  As much as I would like to separate facts from fiction, I am aware that not all the good valid information is written. Not on google webmaster site and perhaps not elsewhere. If so it seems out of date!  Does or does not a WWW domain impact SEO/rank better than its NON-WWW version? (Given that you have setup a proper redirect to avoid duplicates and go with one) Necessary condition for square integrable functions? I'm studying Quantum Mechanics and I came across this which I don't quite understand: For a vector space of functions $f(x)$ to be square integrable (i.e $\int{|f(x)|^2dx &lt; \infty)}$, the necessary condition is $\lim_{|x| \to \infty}f(x) \to 0$. Can someone help me understand why that must be the case? I sort of understand that it must not blow up at the infinities but can a (continuous or piece-wise continuous) function have a non-zero finite value at the infinities and still be square integrable? How to show that a set of discontinuous points of an increasing function is at most countable I would like to prove the following:       Let $g$ be a monotone increasing function on $[0,1]$. Then the set of points where $g$ is not continuous is at most countable.     My attempt:    Let $g(x^-)~,g(x^+)$ denote the left and right hand limits of $g$ respectively. Let $A$ be the set of points where $g$ is not continuous. Then for any $x\in A$, there is a rational, say, $f(x)$ such that $g(x^-)\lt f(x)\lt g(x^+)$. For $x_1\lt x_2$, we have that $g(x_1^+)\leq g(x_2^-)$. Thus $f(x_1)\neq f(x_2)$ if $x_1\neq x_2$. This shows an injection between $A$ and a subset of the rationals. Since the rationals are countable, $A$ is countable, being a subset of a countable set.    Is my work okay? Are there better/cleaner ways of approaching it? $\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$ Can anyone help me with this problem?     Let $f:[0,\infty)\longrightarrow \mathbb R$ be a continuous function such that for each $x&gt;0$, we have $\lim_{n\to \infty}f(nx)=0$. Then prove that $\lim_{x\to \infty}f(x)=0$.   Our teacher told first to prove Baire's theorem, and then show that this is a consequence of that theorem. I proved Baire's theorem, and I spend a few hours thinking on how Baire's theorem is related to this problem, but I couldn't find anything. I'd really appreciate your help. One divided by Infinity? I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it. In this modification of the Monty Hall Problem, instead of three doors, we have four (or maybe $n$) doors, one with a car and the other three (or $n-1$) with a goat each (I want the car).  We need to choose any one of the doors. After we have chosen the door, Monty deliberately reveals one of the doors that has a goat and asks us if we wish to change our choice.  So should we switch the door we have chosen, or does it not matter if we switch or stay with our choice?  It would be even better if we knew the probability of winning upon switching given that Monty opens $k$ doors. Is every discrete absolute value non-archimedean? I've been reading Milne's notes on absolute values and local fields (Chapter 7 of the book on algebraic number theory), and a possibly minor point is confusing me.   On page 126, Milne writes, "$K$ is a field complete with respect to a discrete absolute value $|\cdot|$..." and then he talks about things that only make sense for non-archimedean absolute values, like the ring of integers and its maximal ideal.   Is every discrete absolute value on a field $K$ also non-archimedean? This would explain a lot, but I also suspect that it is not true, because I can't find any statement of this fact anywhere.  EDIT: An absolute value is discrete if the value group $|K^\times|$ is a discrete subgroup of the multiplicative group $\mathbb{R}_{&gt;0}$. An absolute value is non-archimedean if it satisfies the stronger triangle inequality $$ |x+y| \le \max (|x|,|y|) $$ or equivalently if the set $\{|1|,|1+1|,|1+1+1|,\ldots\}$ is a bounded subset of $\mathbb{R}$. Which facility upgrade unlocks maneuver nodes in KSP Performance impact of updating target columns with same values ON CONFLICT This is a question about the inner-workings of Postgres (v10) and performance.  Given a table, github_repos, with a multi-column unique index on org_id and github_id columns, is there any performance difference (or other issues to be aware of) between the two bulk upsert operations below? The difference is that in the first query, the org_id and github_id columns are included in the UPDATE, whereas in the second query they are not. Since the UPDATE runs ON CONFLICT, the updated values of org_id and github_id will be the same as the old values, but those columns are included in the UPDATE because the underlying library I am using is designed that way. I'm wondering if its safe to use as-is or whether I should be explicitly excluding those columns in the UPDATE.  Query #1:  INSERT INTO "github_repos" ("org_id","github_id","name") VALUES (1,1,'foo') ON CONFLICT (org_id, github_id) DO UPDATE SET "org_id"=EXCLUDED."org_id","github_id"=EXCLUDED."github_id","name"=EXCLUDED."name" RETURNING "id"   Query #2:  INSERT INTO "github_repos" ("org_id","github_id","name") VALUES (1,1,'foo') ON CONFLICT (org_id, github_id) DO UPDATE SET "name"=EXCLUDED."name" RETURNING "id"   github_repos table:        Column       |       Type        | Collation | Nullable  -------------------+-------------------+-----------+----------+  id                | bigint            |           | not null |  org_id            | bigint            |           | not null |  github_id         | bigint            |           | not null |  name              | character varying |           | not null |  Indexes:     "github_repos_pkey" PRIMARY KEY, btree (id)     "unique_repos" UNIQUE, btree (org_id, github_id) Is there any way to call the parent version of an overridden method? (C# .NET) In the code below I tried in two ways to access the parent version of methodTwo, but the result was always 2. Is there any way to get the 1 result from a ChildClass instance without modifying these two classes?  class ParentClass {     public int methodOne()     {         return methodTwo();     }      virtual public int methodTwo()     {         return 1;     } }  class ChildClass : ParentClass {     override public int methodTwo()     {         return 2;     } }  class Program {     static void Main(string[] args)     {         var a = new ChildClass();         Console.WriteLine("a.methodOne(): " + a.methodOne());         Console.WriteLine("a.methodTwo(): " + a.methodTwo());         Console.WriteLine("((ParentClass)a).methodTwo(): "          + ((ParentClass)a).methodTwo());         Console.ReadLine();     } }   Update ChrisW posted this:     From outside the class, I don't know   any easy way; but, perhaps, I don't   know what happens if you try   reflection: use the Type.GetMethod   method to find the MethodInfo   associated with the method in the   ParentClass, and then call   MethodInfo.Invoke   That answer was deleted. I'm wondering if that hack could work, just for curiosity.