If I make the tungsten filament in a lightbulbs thicker could it then handle high electricity flowing through it without burning up so fast. Also could making it thick, allow it to handle being cut off and on very rapidly, a few thousands times for hours on end and still not metal? This is for a special fun project I'm working on f.y.I and I need to know if I can make the tungsten filament handle more power at a rapid speed for a very long time.
I want to know, is there a way to make a tungsten lightbulbs filament withstand a mass amount of thermal shock while still producing a vast amount of heat?
If A is a finite set and B is an infinite set, then B\A is an infinite set Prove: If $A$ is a finite set and $B$ is an infinite set, then $B \setminus A$ is an infinite set.   I've tried proving the contrapositive, that if $B \setminus A$ is a finite set then $A$ is infinite or $B$ is finite, but I don't think this is the way to go. Storage order vs Result order This is a spin-off question from .   says this on the subject of storage order (clustered index) and the output order     A lot of people believe that a clustered index guarantees a sort order on output. But that's not what it does; it guarantees a storage order on disk.   See, for example, .   I've read the blog post by Hugo Kornelis and understands that an index doesn't guarantee that the sql server reads the records in a specific order. Yet I have a hard time accepting that I can't assume this for my scenario?  CREATE TABLE [dbo].[SensorValues](   [DeviceId] [int] NOT NULL,   [SensorId] [int] NOT NULL,   [SensorValue] [int] NOT NULL,   [Date] [int] NOT NULL, CONSTRAINT [PK_SensorValues] PRIMARY KEY CLUSTERED  (   [DeviceId] ASC,   [SensorId] ASC,   [Date] DESC ) WITH (     FILLFACTOR=75,     DATA_COMPRESSION = PAGE,     PAD_INDEX = OFF,     STATISTICS_NORECOMPUTE = OFF,     SORT_IN_TEMPDB = OFF,     IGNORE_DUP_KEY = OFF,     ONLINE = OFF,     ALLOW_ROW_LOCKS = ON,     ALLOW_PAGE_LOCKS = ON)   ON [MyPartitioningScheme]([Date])   My original query was this:  SELECT TOP 1 SensorValue   FROM SensorValues   WHERE SensorId = 53     AND DeviceId = 3819     AND Date &lt; 1339225010   ORDER BY Date DESC   But I suggest that I could as well use this one (read below for my explanation):  SELECT TOP 1 SensorValue   FROM SensorValues   WHERE SensorId = 53     AND DeviceId = 3819     AND Date &lt; 1339225010   As you can see, my table rows are small (16bytes) and I've got only one index, a clustered. In my scenario, the table consists of 100.000.000 records at this moment (and this will most likely increase tenfold).  When the database server queries this table it has two ways of finding my rows, either it seeks the primary key and thereby reading and returning my values in desc. order of Date, or it has to do a full table scan. My conclusion is that a full table scan on all those records will be way too slow and the database server will therefore always seek the table via its primary key and thereby returning the values sorted by Date DESC What lens characteristics are important in star photography? In optimal world I would buy a lens that is good in every way. But I'm on a budget and have to find a balance in quality and price. I'm looking for a lens for star photography, so in my case it will be a wide angle lens with good characteristics for capturing points of light in a dark sky. What would those characteristics be?  So far I've learned about , which seems like a thing to note when comparing different lenses for star photography. It would be quite disappointing if stars turned into long teardrops on the edges of a photograph even when every precaution was taken to make all stars sharp round points of light.  Vignetting would be an example of lens characteristic not so important in this use.  Many characteristics of a lens turn better when aperture is slightly stopped down, but I suppose I'd be wanting to use a lens with wide open aperture when trying to capture the stars in a dark night sky.  I'm not asking for lens recommendations. But, as an example of what kind of lenses I've been looking at, I name  manual focus lens. Its price level is $350'ish in Amazon and seems to run with name Rokinon too. It seems to be reasonably sharp even when wide open - my camera is an APS-C sensor camera. I recently wanted to add some RAM to my old computer, but unfortunately I mixed together "good" RAM with chips that I extracted from a computer that failed after getting too much voltage. I know it sounds like a bad idea to just plug it into a motherboard, so I figured I'd ask first - is there usually any protection in the motherboards against this kind of faulty chips? Also, how likely is that RAM got damaged when computer got his deadly current or failed for internal reasons (something shorted because of dust, failed components etc.)? Derivation of binomial coefficient in binomial theorem. How was the binomial coefficient of the binomial theorem derived?  $$\frac{n!}{k!(n-k)!}$$ A new version of Ubuntu has been released. I still can't find it on ubuntu.com. Where can it be downloaded from, or is it the only way to install it using update-manager to upgrade an existing installation? A word that says a person is both female and your friend It's often confusing for me to talk about my friends, especially my female friends. This is because in Dutch there are words for both male ("vriend") and female ("vriendin") friends. In English however, there's as far as I know only the word friend, which can mean both a male or a female friend.  For this reason I was wondering if there is a word to say a person is both female and a friend. Mount error: "unknown filesystem type 'exfat'" When trying to mount an exfat filesystem, I get the following error:  Error mounting /dev/sda6 at /media/gkp/Backup: Command-line  `mount -t "exfat" -o "uhelper=udisks2,nodev,nosuid" "/dev/sda6" "/media/gkp/Backup"'  exited with non-zero exit status 32: mount: unknown filesystem type 'exfat'   Exfat is used on some USB sticks and camera sd cards. What can I do to mount this type of filesystem? How do I bridge network interfaces? I have a laptop running 11.10 with 2 network interfaces, wired and wireless.  Wireless interface connects to the router with DHCP and connects to the internet. Wired interface is connected to a switch. I want the computers on the switch to get their IP addresses from the router not my laptop.     How would I go about setting this up? Bridging the interfaces? Connectedness of the Hausdorff distance. Does anyone know a proof of connectedness of the Hausdorff distance?  I mean a proof of the following:  Theorem  If $(X, \rho )$ is a connected metric space, then $(F(X), d_h )$ is also connected.  Remark:  $F(X) = \{ A \subseteq X | A \text{ is nonempty, closed and bounded } \} $, and $d_h$ stands for the Hausdorff distance. Leave newlines intact in bounty messages Calling a Java method with no name If two people want to buy a car together, would they go half on the car or halves. Example: Let's go half on this car or Let's go halves on this car? what is the [count=\i] in \foreach for? Can someone explain what does [count=\i] in a foreach mean?  Antal S-Z's answer to  use this. It is also mentioned in , but I am not able to locate documentation on this in the TikZ-PGF manual (V2.10) How do I interpret the Mann-Whitney U when using R's formula interface I have a bunch of SD cards that do not have the little plastic switch for the read only setting. so Windows thinks it’s write protected or something. The card is not write protected by the software lock present on the SD card standard.  I’m using one with tape over the notch and it’s ugly. Also, the Thinkpad slot drags on the tape all the time so I’m afraid it will might loose in there eventually.  So, is there any way to tell Windows to ignore this lame write-protect feature?  I’m not interested on the SD card itself as it’s irrelevant for the issue at hand. Read this question as being about a 5.25” floppy disk drive instead of an SD card if you wish. I’m pretty sure the Windows settings are the same for both, really.  I’m  that there are 3 ways to secure an SD card. I’m talking about only the mechanical switch, which is the responsibility of the host to handle. We let a>0 and b>0 and  we have $\sum_{n=0}^{\infty}b^n-a^n$. We have to find all values a,b>0 where $\sum_{n=0}^{\infty}b^n-a^n$ is convergent. I think I can use that $$\sum_{n=0}^{\infty} b_n &lt; \infty , \sum_{n=0}^{\infty} a_n &lt; \infty \implies \sum_{n=0}^{\infty} (b_n-a_n) &lt; \infty. $$. And I think $\sum_{n=0}^{\infty}b^n$ and $\sum_{n=0}^{\infty}a^n$ is convergent if a&lt;1 and b&lt;1? It will make sense. But how can I show it? Image of concave mirror when object is farther than the focal point I have a set of concave/convex mirrors/lenses, and I have drawn out all of the ray tracing diagrams for each possible combination and type of image each optical element can produce. When I look at the ray tracing diagrams then reproduce the situation in the real world with myself as the &quot;object&quot;, all the scenarios make sense to me except one: when I as the object stand beyond the focal point of a concave mirror.  The image ends up as &quot;real&quot; and appears to be in front of the mirror. Now I understand that in the situation above, I as the object would stand at 6m and this would result in the image appearing at 12m. So if I placed a wall or screen at the 12m mark, the image would form on that surface (just like a movie theater screen).... at least I think I interpreted that correctly. But I still see myself when I look in the mirror?! If the image is supposed to form and come into focus behind me, what in the world am I seeing when looking at the surface of the mirror? I still see myself, just inverted. The surface of the concave mirror still has a reflection on it. It doesn't look quite like a normal flat mirror, in that the image doesn't really look like it's &quot;inside&quot; the mirror, more like it's right on the surface of it. It's really frustrating because every other possible arrangement of optical elements makes total sense to me, except this one. Any suggestions on how to think about it? Thank you for your time! Word for sentences that make sense when read backwards? Is there a word for sentences that make sense when read normally or backwards (not necessarily by reversing the words)? Example:     "Are you as bored as I am?" Object rotate in a strange way today i run into another problem. i dont know how i have done it (probably i clicked sth what i should not click) - anyway - since that moment my objects are behaving totally different when i try to rotate them. the objects are now rotating around the pivot point but they keep their alignment - not sure if i am clear. eg. if u would rotate a plane which is lies flat on the ground it makes the rotation but the faces of the plane would still be up and dont which shouldn't be the case with the "normal" rotation that i know. so i want to understand what i have done (because this kind of rotation could be also usefull sometimes for me) and how can i return it in the case it happens again.