What do you call a topological space where a subset is compact iff it's finite? Is there a technical name?  For example, take the discrete topology, or the countable complement topology.
If in a topological space only finite subsets are compact sets, is it then the discrete topological space?   Thank you.
I've created a series of DEM files using the  tool from LAStools; however since I don't have a licensed version they have black streaks running across them. Does anyone know a good method for removing these streaks? convergence to infinity of$ (2^n + 3^n)^{\frac{1}{n}}$ (as $n \to \infty$) Just checking. $2^n$ ($n \to \infty$) tends to $\infty$. + $3^n$ also ($n \to \infty$) tends to $\infty$  so the sum gets me $\infty$.  Now $(\infty)^{1/\infty}$ : $(\infty)^0 = 1$  I see no other way.  Theorem: $n^{\frac{1}{n}} = 1$ as $n \to \infty$.  Analogous:  $(2^n - 3^n)^\frac{1}{n}$ = $(\infty  - \infty)^0$ = 1 ???  Is it ok to suppose infinity on any integer $k^n$ as $n$ goes to infinity ? How can I create an instance of the Java console inside of a GUI panel? Difference between myself and by myself The problem:  Consider the smooth quadric $Q=V(X_{0}X_{1}+X_{2}X_{3}+X_{4}^{2})\subset\mathbb{P}^{4}$ and the line $L=V(X_{0},X_{2},X_{4})$ contained in it. Prove that there exists a vector bundle $F$ on $Q$ with a section vanishing exactly at $L$.  The hardest thing is to get the transition matrices. Any help is appreciated. Order of a homomorphism of groups A quick search for currency regex brings up . The problem I have in choosing one is that regex is difficult to verify without testing all the edge cases. Does anyone have a regex for U.S. currency that has been thoroughly tested? My only requirement is that the matched string is U.S. currency and parses to System.Decimal:  [ws][sign][digits,]digits[.fractional-digits][ws]   Elements in square brackets ([ and ]) are optional.  The following table describes each element.   ELEMENT             DESCRIPTION ws                  Optional white space. sign                An optional sign. digits              A sequence of digits ranging from 0 to 9. ,                   A culture-specific thousands separator symbol. .                   A culture-specific decimal point symbol. fractional-digits   A sequence of digits ranging from 0 to 9. \@seccntformat only for section If $\mathfrak p \subset R$ is a prime ideal, prove that for every nilpotent $r \in R$ it follows that $r \in \mathfrak p$.   The only hint that my tutor gave me was to use induction. Can someone explain what he means by this?  Thanks for the help! Installing python module within code the relationship between maximizing the likelihood and minimizing the cross-entropy How can I test the quality of a RNG? On electronics.stackexchange we had  about constructing a True Random Number Generator. Since the method relies on noise, which isn't deterministic, the only way to test the quality of the RNG seems to be empirical. Not being a statistician I suggested to test a long bit sequence for normality, but I have no idea what outcome is acceptable and what isn't. For instance counting single bits I guess we have a thumbs-up for a 499500/500500 distribution, but when is the ratio too much skewed to be acceptable? Same for 2-bit and longer sequences. Of course, if testing for normality is a Bad Idea™, I'd like to hear it, including better alternatives.    edit Diehard was mentioned a few times, but I'm not sure this answers my question. The normality test should give a normal distribution, with better bell curve approximations for longer sequences. Diehard seems also to have tests which either should result in normal or exponential distributions. But my question remains: how do I judge the results? Just by looking at the curve and discern a bell curve in it? To get back at my first example, a 499500/500500 distribution is definitely OK, and a 950000/50000 distribution definitely is a no-no, so where does the switch-over happen? My usb mouse sleeps after 5 seconds of inactivity when running on battery power. It wakes uo again when i press any button on the mouse. This is really annoying.  I have made lsusb, and I noticed my mouse is   Bus 001 Device 012: ID 04d9:2083 Holtek Semiconductor, Inc.  I have checked my /sys/bus/usb/devices/usb1/power/autosuspend but it is already set to 0, and the directory usb1 has many subdirectories which also have autosuspend files, and i dont know how to edit them.  Also, I would like a permanent solution, which would work for any mouse, on any of my 3 usb ports. Any ideas?  Using: Ubuntu 12.04 64bit A limit ordinal $\gamma&gt;0$ is said to be indecomposable iff $\nexists\alpha,\beta&lt;\gamma$ such that $\alpha+\beta=\gamma$.  In view of this definition, I’m trying to prove the equivalence of the following statements for limit ordinals $\gamma$:  (1) $\gamma$ is indecomposable.  (2) $\alpha+\gamma=\gamma$ $\forall\alpha&lt;\gamma$.  (3) $\gamma=\omega^\alpha$ for some $\alpha\in\mathrm{ON}$.  I’ve been able to get $(1)\implies(2)$ and $(3)\implies(1)$, but I have nothing more than scratch work for $(2)\implies(3)$.  Any suggestions would be appreciated. How to use "grep" command to find text including subdirectories I'm pretty new to this and this is my first question here, any help would be greatly appreciated.  So basically what I want to achieve is a floor material as seen in this photo...    ...the reflections are very crisp but dim.  With a glossy shader I get the following results:    First picture: reflections are blurry  Second picture: roughness of the material looks right but reflection is bright red  Third picture: If tinted in any other color than white, it seems to produce the result I want. Reflection is sharp and gets tinted blue. What I need is the reflection to be tinted white.  Thanks for any help. Pokemon Go Supported Devices One of the products being shown a CES is a  intended to let you charge a tablet from a laptop USB port that normally wouldn't work because it didn't provide enough power.  The CNET writeup implies that it's actually boosting the power output from the port beyond the normally available amount.  This seems improbable to me because the ports should have current protection to protect themselves from shorts.  Also, if it was possible to bypass the current limit externally, I'd've expected at least some tablet vendors to have included the ability to do so directly in their cables.  One possibility that occurs to me is that the dongle is just spoofing responses to the tablet when it queries the laptop about the maximum power it can deliver while only providing a trickle charge that the tablet would otherwise reject as too slow to bother with. Motivation for spectral graph theory. How do you find the modular inverse of $5\pmod{\!11}$