How to dynamically generate methods and properties with Python?
Adding a Method to an Existing Object Instance
An element not in a field extension Possible Duplicate:          Consider the field extension $\mathbb{Q}(\sqrt2)$. I want to show that $\sqrt5 \notin \mathbb{Q}(\sqrt2)$. If this were not the case, then we could write $\sqrt5 = a + b\sqrt2$ for $a,b\in\mathbb{Q}$. However, I do not see the contradiction here. Is there a better/easier way to prove this? Suppose that $f$ is holomorphic on $\mathbb C$ and that $\Re(f(z))\ge 0$ for all $z$. Show that $f$ is constant. [Hint: consider $e^{−f(z)}$.]   My thoughts: If $\Re(f(z))\ge 0 $ holds, then $e^{−f(z)}$ is a bounded holomorphic function (do I need to prove this or is it obvious?) So then by Liouville's Theorem $e^{−f(z)}$ is constant.   But then I'm not sure how to rigorously go from this $\exp(−f(z))$ back to $f(z)$.   Could anyone help me piece this together please?  Thanks Is it ethical to use a recommendation letter from a deceased professor? She was a really nice professor and she wrote me a good recommendation letter that resulted in a lot of good results with applications. Recently, this professor died from brain cancer, which was a fast and shocking death for me.  Tomorrow is the deadline for a grant. What should I do? Is it professional to use letters from the deceased? How to measure supply currents ranging from 1μA to 10mA? Energy conservation of Virtual Particles - Quantum Fluctuation? I (as a middle-school student) was wondering how virtual particles even conserve energy of the entire system? I don't mean just the particle's energy, but conservation with respect to the surroundings?  Let me explain more, Einstein proved that $E = mc^2$ and equivalently, we can say $m = \frac{E}{c^2}$ . We however know mass causes curvature in space-time (gravity well). Now that statement being completely valid we can use Quantum Fluctuation, implying energy and time can be related by the relation:  $\Delta{E}\Delta{t}\approx\frac{\hbar}{2}$ and by that simple relation we can make the following points:   As the energy increases, the time allowed to be "borrowed" decreases, before it gives it back to the universe. As time increases, the energy allowed to be "borrowed" decreases.    These are completely satisfactory points I've made, I believe.  Now, I have read that the vacuum is filled with constantly bubbling virtual particles that get created from the energy "borrowed" by the above relation and is destroyed again, which satisfies the energy conservation laws.   This seems to imply that  in the short time the virtual particle exists, they must have a very small mass which is: $m_{1} = \frac{\Delta{E}}{c^2}$ and using basic classical mechanics rather than GR (for sake of simplicity) we calculate that the gravitational force mediated by this short-lived virtual particle;  $F_{g}= G\frac{m_1 * m_x}{r^2}$   where $m_x$ is an particle\mass in question. Nevertheless since we know the force set upon an object moves the object in a direction, we can say it would increase its kinetic energy by this factor: $F_g = \frac{1}{2}mv^2$ which is equal to $G\frac{m_1 * m_x}{r^2} = \frac{1}{2}mv^2$.  Surely, this implies that every time quantum fluctuations happen, energy of real-particles\masses increases and therefore violates energy conservation, but what prevents this violation from taking place?  If virtual particles are not really present and interact with objects like I thought, how can Hawking radiation (currently a large concept in black hole physics) then be accepted in physics community? Is the function $f(x)=|x|^{1/2}$ Lipschitz continuous? Is the function $f(x)=|x|^{1/2}$ Lipschitz continuous near $0$? If yes, find a constant for some interval containing $0$.   I think the answer is yes since I can find $L=1$ that satisfies Lipschitz continuity criteria in a interval close to $0$, am I right? Initially, my question was: is "focussed" or "focused" the correct past tense of "focus", but since this applies to a lot of words, I would like to generalize and ask: is there supposed to be a rule when to double the consonant? My Realtek NIC in my Windows Home Server (essentially w2k3) box refuses to run at 1000Mb/s even if I change the driver settings from Auto Negotion to 1000Mb/s full duplex. I've installed the latest driver and tried changing the speed setting but I'm having no luck. Not sure what to try next. Any ideas?  I have a Netgear GS605 v2 Switch supports 10/100/1000 D Link DIR 655 router.  All my machines bar one/2 have 1000Mb/s NICs (Old laptop/Xbox being the exceptions)  The reason I noticed the problem was because I was copying files between two machines and maxing one NIC out and only seeing 10% on the other machine. I do have a fairly lengthy cable between the switch and the router (maybe 20m) could that be the issue? $\lim\limits_{n\to \infty} \int_0^1 |f(x)-a_nx-b_n| dx=0$ implies $(a_n)_n,(b_n)_n$ are convergent Let $f:[0,1] \to \mathbb R$ be a continuous function and the sequences $(a_n)_n,(b_n)_n$ s.t. $$\lim_{n\to \infty}  \int_0^1 |f(x)-a_nx-b_n| dx=0.$$ Prove that $(a_n)_n,(b_n)_n$ are convergent.   I know that $$\left|\int_0^1f(x)dx\right| \le \int_0^1|f(x)|dx.$$ Can somebody help me, please? I have recently upgraded my OS to Ubuntu 18.04 (fresh install via boot device). However, when trying the command:  sudo apt-get upgrade   It works fine until ~75% when it stops and says:  snapd.snap-repair.service is a disabled or a static unit, not starting it.   I'm not quite sure what this means and if I Crtl-Z to get out of it, any time I try to install anything I get:  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?   and have to restart my computer to install anything. Is it time to be rid of automatic down votes on certain closed questions? Right now,  carry automatic downvotes.  The  for this was largely to enforce specific quality bans in part because people were not down voting questions. Now that question down votes are free on questions and it seems to be pretty commonplace for question quality bans to trigger, even without the automatic votes from closure, and we have completely revamped the closure system. Is it time to reevaluate whether or not these automatic votes are still a good idea?  What benefits do the automatic votes provide and have they effectively run their course? Call native javascript function that has been "erased" by the web page Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$ Prove that for any natural number $n&gt;1$, we have $(2n)!&lt;(n(n+1))^n$    I tried using induction, but I failed in that approach, I rather found it was untrue, but on several case testing, I found it to be true. I am out of ideas here, please help. Thank you. How to remove uninstalled snaps from cache? I have the following text:    A   Hello   world   B   Hello   world   C   Hello   world   I know that I can replace Hello by Hi using sed:  sed 's/Hello/Hi/g' -i test   but this replace each Hello with Hi:    A   Hi   world   B   Hi   world   C   Hi   world   what I really want is to replace only the Hello after B:    A   Hello   world   B   Hi   world   C   Hello   world   so I have tried this:  sed 's/"B\nHello"/"B\nHi"/g' -i test   but nothing happened, How can I do this?  Note: There are some white-spaces on the beginning of each line of the file. How do we "restore" notepad after crash? I was running NotePad and Chrome when my computer suddenly shuts down.  After reboot, chrome was able to "restore" itself such that I didn't lose any data.  However, how do we "restore" notepad.exe? Add a time limit before you can vote on a post There needs to be a timer or something on upvoting/downvoting.  I posted an answer to a question and as soon as the page loaded, my answer was already down voted. There is no way someone had the time to read the answer &lt; 10 seconds after it was posted. Is there console mode in Mac OS X? 'AND' vs '&&' as operator "Open shaming of anyone..." Open shaming of anyone who spoke out discouraged responsible dissent.   How does open with shaming work, grammatically and meaningfully?   Is discouraged modifying "responsible dissent?