If $\dfrac {x} {\infty }=0,$ where $x$ is a finite number, than wouldn't $0\cdot \infty $ be equal to any number? Making this not work?
I did a bit of math at school and it seems like an easy one - what am I missing?  $$n\times m = \underbrace{n+n+\cdots +n}_{m\text{ times}}$$  $$\quad n\times 0 = \underbrace{0 + 0 + \cdots+ 0}_{n\text{ times}} = 0$$  (i.e add $0$ to $0$ as many times as you like, result is $0$)  So I thought an infinite number of $0$'s cannot be anything but $0$? But someone claims different but couldn't offer a reasonable explanation why. Google results seemed a bit iffy on the subject - hopefully this question will change that.
Let $V$ be a finite dimensional vectorspace over a field $\mathbb{ F}$. It's easy to show that if $U$ and $V$ are subspaces of $V$ then $U \cap V$ is a subspace. But what if there are an infinite number of them? I have seen sometimes in pure maths that you take an arbitrary finite collection of sets and show the statement you are trying to prove is true for them to deduce it is true for the whole infinite collection. Why is this technique allowed? Can I do it for this case? Why? I understand that there is an upper limit. But why do you have to type at least 15 characters to post a comment? It is easy to work around it anyway (like adding dots or other useless things). Given an integer $n$, we are asked to investigate about the existence of integer divisors of $n^2+1$ of the form $4k+3$. Can you provide some insights about it? Debug JavaScript within IE6 How to change permissions of multiple files found with find command? It seems that in the words Englishman, Frenchman, and Scotsman, the ‑man part is pronounced /mən/ (just like in Roman).  Whereas in snowman, the ‑man part is pronounced /mæn/ (just like in no man).  Why is it that when ‑man is appended to snow‑ to make snowman, the pronunciation of the man part doesn’t change?    Wouldn’t it logically follow for it to be pronounced /ˈsnowmən/ not /ˈsnowˌmæn/? What size canvas should logos be designed on? When designing a logo is there a minimum size canvas that should be used to keep quality when it is enlarged or when reduced?  Obviously the dimensions of a canvas depend on the shape of the logo, but is there a sugested size? File1:  .tid.setnr := 1123  .tid.setnr := 3345  .tid.setnr := 5431 .tid.setnr := 89323   File2:  .tid.info := 12 .tid.info := 3 .tid.info := 44 .tid.info := 60   Output file:  .tid.info := 12 .tid.setnr := 1123 .tid.info := 3 .tid.setnr := 3345 .tid.info := 44 .tid.setnr := 5431 .tid.info := 60 .tid.setnr := 89323 Cut part from video file from start position to end position with FFmpeg I have a video file of 30 minutes, but I want to extract a video from 00:09:23 to 00:25:33.   I can define the startposition with -ss, but I couldn't find one for the end position. Any help please? Best Place to put Feature Requests? UNO Stacking a Draw 4 Card instead of picking up 4 cards? Need clarification on the Draw 4 rule. - Player 1 lays down a Draw 4 Card and says the color is Red. - Player 2 does not have a Red card but has a Draw 4 Card. Can Player 2 lay down his Draw 4 Card and have Player 3 draw 8 cards? Fundamental group of a torus with points removed How can I tell if sheet a exists in a workbook? I have the following code that's not working as expected:  If Sheets("a") &lt;&gt; "" Then MsgBox ("sheet a exists")   How can I tell if sheet a exists in the workbook? Given the size of the Empire, it seems highly probable that names would be reused. Although I'm not aware of any in canon, there must be other Skywalkers in the galaxy, leading me to my question.  Are there other Skywalkers in the galaxy, and are they mentioned in canon? Does Luke have any third cousins twice removed (etc.)?  Bonus points if you can attest to force sensitivity among the surname. (semi)-Automatic pluralization around a citation The integral $\int_0^8 \sqrt{x^4+4x^2}\,dx$ How do we see? Where do the photons disappear? terminal: non-english characters I used to be able to copy&amp;paste (or type if I load respective keyboard layout) any kind of characters (eg. é ö ñ ß و 好) in my console/terminal.  Now I bought a new computer and it does not work any more, only English/ASCII characters (but in other programs, e.g. firefox, it still works).  Distribution: Ubuntu. Terminals tried: gnome-terminal, xterm, konsole.  I tried  but after reboot echo $LANG still gives C. I also tried setting Character encoding to Unicode(UTF-8) in the gnome-terminal Terminal-menu - without effect.  Question: How can I get a terminal that is able to deal with non-English characters? Creating square buffer around point feature using ArcGIS for Desktop? I would like to create a square buffer from a point feature but I do not understand the code that goes into it.   Similar questions have been asked on the forums.esri website but that was over 10 years ago, and it did not work when I tried the code.  How do I create a square buffer from a point feature? Just need help understanding this question, as I don't really understand what a continuous random vector is. My limited understanding is that a continuous random vector must be completely continuous (so for continuous X and Y this is satisfied) and that to get the probability of the random vector occurring, we double integrate over the supports (of X and Y obviously). My guess is then, that the c.r.v (X,Y) IS a continuous random vector.  Also, what of the converse? If (X,Y) is a continuous random vector, then are X and Y continuous random variables? I also think this is correct, as the continuity of the vector MUST imply the continuity of X and Y, although I'm honestly not sure.  Thanks