Cauchy implies monotone + bounded
Show that every monotonic increasing and bounded sequence is Cauchy.
How to add some non-standard font to a website? Is there a way to add some custom font on a website without using images,  or some other graphics?  For example, I was working on a wedding website, and I found a lot of nice fonts for that subject. But I can't find the right way to add that font on the server. And how do I include that font with CSS into the HTML? Is this possible to do without graphics? Are there fields and ordered fields of every infinite cardinality? On the top of my head, I cannot think of any fields of cardinality more than that of the reals. (It is known that the process of algebraic closure does not increase the cardinality of an infinite field.)  What is the simplest way to give an example of a field (and an ordered field) of a specific cardinality $\alpha$?  I see there is the "Field" of surreal numbers, but it is a proper class rather than a set (and hence do not have a cardinality as such). However, there seems to be some modified construction which gives proper fields with the cardinality of some strongly inaccessible cardinal. How can I test whether my camera is working after it was dropped? Issue : How can I evaluate my cameras performance synthetically?  Scenario : Bought a Nikon D3100 an year back. Photos looked good enough. The camera fell, zoom lens effected.  But works. Cleaned lens using soap, water etc.  Carefully. Now photos look much worse.  How do I know if Photos are really bad?  Is there a tool?    Sample Photo  Now (Bad)   Original (Good)   Please help me realize whether my camera has gone bad.  Can you tell your personal opinion also? How to force a node group input field to display a slider? I have created a couple of node groups with some "group-inputs-sliders" (The one called "Roughness" in the bottom picture). I would like it to have the blue-bar slider like the blender native ones. Thanks (: How old is Chewbacca, anyway? Do Wookiees get gray fur when they are old? Is there a way to create synchronization profiles for Google Chrome? For example I want to tag some of my browsers as "home browser"s and others as "work browser"s and I want:   my bookmarks to be synced with all browsers, my extensions to be synced only within browsers of the same type (home with home, work with work) Introduction to statistics for mathematicians What is a good introduction to statistics for a mathematician who is already well-versed in probability?  I have two distinct motivations for asking, which may well lead to different suggestions:   I'd like to better understand the statistics motivation behind many problems considered by probabilists. I'd like to know how to better interpret the results of Monte Carlo simulations which I sometimes do to form mathematical conjectures.   I'm open to the possibility that the best way to go is not to look for something like "Statistics for Probabilists" and just go to a more introductory source. Should I postpone my trip to Paris in 2nd week of Jan in light of recent protests? I’ve a date and I really waited long to make this happen. My gifrfriend is a bit worried about the security issue in Paris. Which locals think that the media is exagerrating the issue and the issue is small and non-threatening for tourists? I'm having trouble understanding the simple voltage regulator that can be built using a zener diode (from section 2.04 in the Art of Electronics).  I know that it would be better to use amplifiers, et cetera, but I'm just trying to understand how this circuit works.      I don't really understand how the circuit works, but I am guessing that when a load is applied to the output, it drains current from the source (Vin) and thus causes the voltage to drop?  How does the zener diode help to maintain the voltage and thus make this circuit act as a regulator? "there doesn't seem" vs. "there don't seem" "Dark L" is "L" at the end of the word or after a vowel sound. Example: ball, pull.  "Light L" is "L" at the beginning or before a vowel sound. Example: light, love.  There are 4 explanations of how to pronounce "dark L":   1st explanation: the tongue tip must contact the ridge right behind the upper teeth. 2nd explanation: before the tongue tip must contact the ridge right behind the upper teeth, you must curl the tongue and make sound like /r/ before make the /l/ as in the 1st explanation. 3rd explanation: just put the tongue between upper and lower teeth is enough to make the dark L 4th explanation: the tongue tip must contact the ridge right behind the upper teeth &amp; the back of the tongue raises up (a British teacher teaches that).   see this vid:  and  for more info  So what is the correct way to make the "dark L"? How to completely disable the Windows taskbar? I've installed Taskbar eliminator, while it works most of the time, alerts being the taskbar back.  I've also installed object dock which can disable the taskbar, object dock appears during window changes.   Has anyone had any luck permanently removing, hiding the taskbar in Windows 7?  Update  I found an application that seems to be working here:    Second update  I took the leap and installed a shell replacement (). So far so good. I have a chain object. And i have a curve it follows. I got it to work for following curve, but chain object is not circles but both parts are more like stretched circles (ovals). Object i made with 2 toruses one rotated 90 degrees and then joined them together. I tried single torus too. But same issue. on a curve it just looks stretched oval. What can be the issue?   Thanks Is a general GRE score of X sufficient for entry to postgraduate degree Y? Question: I got general GRE scores of VR (verbal reasoning), QR (quantitative reasoning), and AW (analytical writing).  Is this a good score to apply for entry to postgraduate degree in field X?  How will this score look to the selection committee?    Note: This is an intentionally generic GRE question (with unspecified scores and field of study) which is intended as a template for a large number of questions asked on this forum regarding evaluating the scores on the general GRE test (e.g., , , , , , , , and ).  This question seeks answers that are applicable for an applicant for graduate-level programs in any field, based on any scores in the GRE general test.  The goal of this question is to provide a general reference to avoid the need for specific questions with particular scores/field of study. Is there a way in Java to have a map where the type parameter of a value is tied to the type parameter of a key? What I want to write is something like the following:  public class Foo {     // This declaration won't compile - what should it be?     private static Map&lt;Class&lt;T&gt;, T&gt; defaultValues;      // These two methods are just fine     public static &lt;T&gt; void setDefaultValue(Class&lt;T&gt; clazz, T value) {         defaultValues.put(clazz, value);     }      public static &lt;T&gt; T getDefaultValue(Class&lt;T&gt; clazz) {         return defaultValues.get(clazz);     } }   That is, I can store any default value against a Class object, provided the value's type matches that of the Class object. I don't see why this shouldn't be allowed since I can ensure when setting/getting values that the types are correct.  EDIT: Thanks to cletus for his answer. I don't actually need the type parameters on the map itself since I can ensure consistency in the methods which get/set values, even if it means using some slightly ugly casts. How does Newtonian gravitation conflict with special relativity? In the Wikipedia article , it says     After Newtonian gravitation was found to be inconsistent with special relativity, . . .   I don't see how Newtonian gravitation itself is inconsistent with special relativity.  After all, Newton's Universal Law of Gravitation is completley analogous to Coulomb's Law, so it would seem that, if there were an analogous "gravitational magnetic field", one could formulate a theory of gravitation in exact analogy with Maxwell's Theory of Electromagnetism, and of course, this would automatically be consistent with Special Relativity.  What about this approach to gravitation does not work?  The only problem I could see with this is the lack of evidence for a "gravitational magnetic field".  That being said, gravity is "weak" as it is, and my guess is that it would be extremely difficult to set up an experiment in which a massive body were moving fast enough for this "magnetic field effect" to be obsevable.  EDIT:  As has been pointed out to me in the answers, Newton itself is inconsistent with SR.  Similarly, however, so is Coulomb's Law, yet, electromagnetism is still consistent with SR.  Thus, how do we know that it is not the case that Newton's Law is the special "static" case of a more general gravitomagnetic theory exactly analogous to Maxwell's Theory:  Let $\mathbf{G}$ be the gravitation field, let $\rho$ be the mass density, and $\mathbf{J}$ be the mass current density, let $\gamma _0$ be defined so that $\frac{1}{4\pi \gamma _0}=G$, the Universal Gravitation Constant, let $\nu _0$ be defined so that $\frac{1}{\sqrt{\gamma _0\nu _0}}=c$, and suppose there exists a field $\mathbf{M}$, the gravitomagnetic field, so that the following equations hold: $$ \vec{\nabla}\cdot \mathbf{G}=-\frac{\rho}{\gamma _0} $$ $$ \vec{\nabla}\cdot \mathbf{M}=0 $$ $$ \vec{\nabla}\times \mathbf{G}=-\frac{\partial \mathbf{M}}{\partial t} $$ $$ \vec{\nabla}\times \mathbf{M}=\nu _0\mathbf{J}+\gamma _0\nu _0\frac{\partial \mathbf{G}}{\partial t} $$ where theses fields would produce on a mass $m$ moving with velocity $\mathbf{v}$ in our inertial frame the Lorentz force $\mathbf{F}=m\left( \mathbf{G}+\mathbf{v}\times \mathbf{M}\right)$.  This theory would automatically be consistent with SR and would reduce to Newton's Law of Gravitation for the case of gravitostatics:  $\frac{\partial \mathbf{G}}{\partial t}=\frac{\partial \mathbf{M}}{\partial t}=\mathbf{J}=0$.  (To be clear, you can't just set the time derivatives equal to $\mathbf{0}$ as it seems I have done.  Upon doing so, you obtain the corresponding static theory, which is technically incorrect (as you can easily see because it won't be relativistically invariant), but is nevertheless often a useful approximation.)  My question can thus be phrased as:  without appealing directly to GR, what is wrong with this theory? Agent Smith, in the first Matrix movie (The Matrix) talks about how the machines originally created a paradise setting and humans didn't accept it, so it went back and created a more realistic one that humans would accept.  The human bodies, as we've seen, are kept in tanks and the body is kept asleep.  But why did the Matrix need to provide any kind of simulation for the brain to experience?  Why couldn't it have just kept all humans in a medically induced coma?  Or performed something equivalent to a lobotomy on every human?  Why did the Matrix need to spend the resources to keep the humans in good mental shape? If you get stuck in research, at what point in time should you ask for help? It's always worthwhile to take some time to try to figure it out by yourself. But eventually there's a point where you're unsure how much more time it would take to figure it out by yourself (which could take far longer than you originally think), and when asking for help could be more helpful.  So for analytical or computational research, what are some guidelines for when you should ask for help (from either your adviser, other grad students, or other researchers) when you get stuck? Extract Raster Value into Polygon Attribute I have Raster Data for a State which has Elevation Data in its pixels. I also have Vector layer which has the 300 divisions of State. what I need is, I want to get the average elevation value of particular division from the raster data using ArcGIS. I tried extract by mask in ArcGIS to extract individual polygon to clip the raster into 300 raster then from individual raster i have collected average elevation but it has taken days together to complete the work. Is there any other easy way to get it? How to use iSight webcam without activating the green light? Recently a the Dutch government advised to put a tape on your webcam to prevent hackers from taking pictures and video using your device ().  The build in iSight camera in Apple laptops have a green light next to the camera, this light turns green when you use the camera.  Is it possible to use the camera without the activation of the green light? Personally I think the green light turns on when the sensor requires power and this is hardwired in the hardware. Am I wrong?  I have found similar questions on stackexchange, but I found non that answer this specific question.