How to prove that the following metrics are topologically equivalent
Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces
I only ask questions. Am I unwanted? Possible Duplicate:          I've been  for maybe a year to get answers to questions I couldn't find on my own.  I always make an attempt first to find the answer on my own.  As of this posting, I've asked 14 questions.  I only once gave an answer, and it was to a non-technical question, and only because I was really bored and had too much coffee to drink.  I wasn't intending to answer any other questions in the future, because on on my best days I'm only a mediocre programmer, and there are some real geniuses here on StackOverflow who can answer other peoples' questions faster and more accurately than I can.  It actually is my nature.  I am an Aquarian.  We are asker-listeners.  Today I discovered Meta Stack Overflow and started browsing around.  I became familiar with the concept of the "Help Vampire".  I seem to qualify.  I continued reading more posts on the topic and got the distinct impression that people who only ask, and never answer, are less than welcome here, rather despised.  So, should I just go away?  Or should I start contributing answers just to have a answer-to-question ratio of 3-to-1 (I read somewhere that's the average) even though I am less than one eighth as knowledgeable as the 10K+ guys and gals?    Or should I continue as I have begun?  I mean, doesn't a 0-questions-asked user like Jon Skeet need a Blankman?  Yin and yang, you know? Would it be possible to have a "community accepted" feature? About the localization of a UFD I was wondering, is the localization of a UFD also a UFD?    How would one go about proving this? It seems like it would be kind of messy to prove if it is true.  If it is not true, what about localizing at a prime? Or what if the UFD is Noetherian? In the series finale, Admiral Janeway travels back to 2378 to take Voyager back to Earth. Out-of-universe, of course, this point in time was chosen to fit in with the continuity of the rest of the series. In-universe, however, it seems that Janeway could have chosen any point in time, since she had the ability to travel to and from the Delta Quadrant at will. Is there a reason given, in-universe, for why she chose that particular incident to travel back to? Proof of the following inequality $ \frac{x - y}{\log x - \log y} > \sqrt{xy} $, $x>y$. I have seen the following inequality  $$ \frac{x - y}{\log x - \log y} &gt; \sqrt{xy} \ , \quad \forall x&gt;y $$ be stated as a near "obvious" fact in another , on the site.  The inequality is very cute, but so far I have not been able to prove it.  It reminds me of the Lipschitz inequality, but has some minor differences. Also Jensens inequality comes to mind. Is there something obvious I am missing, or is this ineqality not as easy to prove as it looks? Is empty set element of every set if it is subset of every set? This problem is from Discrete Mathematics and its Applications  My question is on 9b. I know that the sign represents an element is a member of. (from book)  I know that the O with a slash across it is the empty set which &quot;is a special set that has no elements&quot;. From , I got that the empty set is a subset of all sets, meaning that every member of the empty set(nothing) is also a member of any other set. Based on all of this, for 9b, would {0} contain the empty set because it fundamentally has the elements that consist of the empty set(nothing) or does it physically have to have the empty set? How would one create an iterative function (or iterator object) in python? New Zealand pronunciation of "women" vs "woman" I have read in a number of places that the NZ pronunciation of "women" must be rather peculiar. Quoting from :     For some years I've noted the tendency of Kiwis to pronounce "woman" and "women" identically (as "woman").   To which an Australian replies:     It appears there is a vowel shift going on in New Zealand (NZ) English [...] [T]he vowel in "women" which in Australian English is the same as the vowel in "hit", is often, in NZ, reduced to a schwa [...]. It makes the plural sound like our singular. I don't think the NZ pronunciation of the singular is the same as the NZ plural   A New Zealander begs to differ:     I've noticed this trend over the last few years also. To me as a kiwi it doesn't sound anything like a mispronounced plural -- it just sounds as if the speaker is using the one word for both singular and plural. [...] I see it as part of a much larger tendency to confuse singular and plurals. [Several examples follow.]   Who's right? Who's wrong? Wikipedia has :     In New Zealand English the short i of KIT is a central vowel not phonologically distinct from schwa /ə/, the vowel in unstressed "the". It thus contrasts sharply with the [i] vowel heard in Australia. Recent acoustic studies featuring both Australian and New Zealand voices show that the accents were more similar before the Second World War and that the KIT vowel has undergone rapid centralisation in New Zealand English. Because of this difference in pronunciation, some New Zealanders claim that Australians say "feesh and cheeps" for fish and chips while some Australians counter that New Zealanders say "fush and chups".   So, there appears to be a vowel shift going on; but I'm not sure if there might be some truth to the people-just-stop-caring-about-certain-plurals argument as well.  I hope we have enough New Zealanders on board to shed some light on this.   Can you provide a guide to how to pronounce "women" and "woman" in NZ English? (I've done some searching for audio files or YouTube videos, but haven't found anything yet.)  Would you say that it's just the vowel shift, "a much larger tendency to confuse singular and plurals", or both?  How recent is this trend? (E.g., if you are a native speaker of NZ English, is your pronunciation of "women" different from that of your parents/grandparents?) Long sites break the layout on the front page The long name pushes the stats to a weird place. And what's with the "Stack Exchange" at the end anyway? How do I color intersection of two ellipses in different color. For instances, the ellipses should themselves be colored as yellow and their intersection as red. My code for drawing ellipses is given below  \draw (-4,0) ellipse (8 and 3); \draw (8,0) ellipse (8 and 3);   UPDATE: In the comments to individual answers, I have requested to show it for three ellipses. Syntax error while creating DB2 Trigger What is wrong in the below trigger syntax, I am getting this error An unexpected token "INT" was found following " DECLARE NULL_ROW_ID".  Expected tokens may include:  "END-OF-STATEMENT".. SQLCODE=-104, SQLSTATE=42601, DRIVER=3.68.61  CREATE TABLE A (     A_ID INT NOT NUll,     A_CODE VARCHAR(100) NOT NULL,     PRIMARY KEY(A_ID) );  CREATE TABLE B (     B_ID INT NOT NUll,     B_CODE VARCHAR(100) NOT NULL,     A_ID INT,     PRIMARY KEY (B_ID),     FOREIGN KEY (A_ID) REFERENCES A (A_ID)  );  CREATE OR REPLACE TRIGGER B_TRIGGER AFTER UPDATE OF A_ID ON B REFERENCING NEW AS N OLD AS O FOR EACH ROW     WHEN (N.A_ID IS NULL)     BEGIN ATOMIC         DECLARE NULL_ROW_ID INT;         SET NULL_ROW_ID = (SELECT A_ID FROM A WHERE A_CODE = 'Custom Null String');         IF NULL_ROW_ID IS NULL THEN             SIGNAL SQLSTATE '70000' SET MESSAGE_TEXT = 'Custom Null String row not found.';         END IF;     SET N.A_ID = NULL_ROW_ID;     END @   It's on DB2 Express-C 10.5 Proof of $\pi$ not being a quadratic irrational number. Does someone know a proof (books, articles) that $\pi$ is not a quadratic irrational?   The proof should not use that $\pi$ is transcendental.  Any hints would be appreciated. What is the name of the package for R? I tried aptitude search r, but (unsurprisingly), there are waaaay too many results to sift through. Why does Vader live on Mustafar? In Rogue One, we get our first glimpse of Darth Vader's primary residence - a castle on Mustafar.  Given the freedom to choose any planet in the galaxy as their new home, I don't think many people would pick the place where they had three limbs chopped off, fell into a lava flow, and were burned alive, but this appears to be what Vader did.   Why does Vader live on Mustafar of all places? How to modify font for all text fields? How to delay or slowly loop commands? What are bitwise operators? I'm someone who writes code just for fun and haven't really delved into it in either an academic or professional setting, so stuff like these bitwise operators really escapes me.  I was reading an article about JavaScript, which apparently supports bitwise operations. I keep seeing this operation mentioned in places, and I've tried reading about to figure out what exactly it is, but I just don't seem to get it at all. So what are they? Clear examples would be great! :D  Just a few more questions - what are some practical applications of bitwise operations? When might you use them? Navigating lookup relationships with dot notations, to retrieve field values I need to access the value from a roll-up field on my Opportunities, from it's related Opportunity Product.  When I use oli.Opportunity.Software_Line_Item__c the value retrieved is always null.  So I've also tried oli.OpportunityId.Software_Line_Item__c which causes an error in the compiler     Invalid foreign key relationship: OpportunityLineItem.OpportunityId   &amp; just to make sure that it's not the roll-up field calculation that's not working as expected, I've tested oli.Opportunity.Name which is also returning null.  I know this is basic but I don't have Eclipse installed so I can't check the correct reference to use. Could someone please let me know how I can navigate this relationship, to retrieve the value from the Software_Line_Item__c field? What is the maximum number of downvotes a question can have I was just wondering what the maximum number of down votes a question can have before it is removed from StackOverflow. How to stop fluid inflow? I have fluid simulation with an inflow object. I want the inflow to go for 2 seconds, then have the inflow stop (so no more fluid is added) but keep the simulation going  (so the existing fluid sloshes around).  However, I do not see any way to set start and ending values on my inflow object.  How do I stop inflow at a certain frame/time in my simulation?