I'm learning python and I'm finding python methods inconsistent.  Why is it that Len is len(s) whereas if I want to read a file I do f.read() and why do I have os.read() which is completely different that f.read().  What's the rationale of having such inconsistency in python.  Why cannot I do s.len() just like I can do f.read()? Why does os.read() exist when f.read() exists.
I know that python has a len() function that is used to determine the size of a string, but I was wondering why it's not a method of the string object.  Update  Ok, I realized I was embarrassingly mistaken. __len__() is actually a method of a string object. It just seems weird to see object oriented code in Python using the len function on string objects. Furthermore, it's also weird to see __len__ as the name instead of just len.
Is trace of regular representation in Lie group a delta function? My major is physics. I need to use some tools in group theory, but I am really  confused by the trace in compact infinite groups. The following is my question:  In discrete group theory, the irreducible representation of identity group element $e$ is always an identity matrix. So the trace of $e$ under  regular representation is the order of the group : $\chi(e) = |G|$. I hope to get  similar result for Lie group. For example, SO(2) has infinite number of irreducible representations, $D^{(m)}$, where $m=0,\pm 1, \pm 2,\cdots $. All of them are 1-dimensional $D^{(m)} = e^{im\phi}$. Here $\phi$ is the rotation angle. For element $R(\phi)$ in SO(2), the trace in $m$th irreducible representation should be  $\chi(R(\phi))=e^{im\phi}$, if we sum all these traces up, we get the trace in regular representation. So what is the trace of $e$ in the regular representation ? It seems to be infinite. What are the light blue lines on my imported objects The computed moments of log normal distribution can be found . How to compute them? I am new to TeX/LaTeX. How do I install TeX on Windows (7)? It seems that there are many different implementations, so which one is best for my OS? How can I use multiple accounts with Telegram? Is there a way to have two copies of  app in Ubuntu each with a different account?  It seems copying the app in another folder does not work. To show that $\sum a_nb_n$ is absolutely convergent Evaluate the limit $\lim\limits_{n \to \infty} \frac{1}{1+n^2} +\frac{2}{2+n^2}+ \ldots +\frac{n}{n+n^2}$ Evaluate the limit   $$\lim_{n \to \infty} \dfrac{1}{1+n^2} +\dfrac{2}{2+n^2}+ \ldots+\dfrac{n}{n+n^2}$$   My approach :   If I divide numerator and denominator by $n^2$ I get :   $$\lim_{ n \to \infty} \dfrac{\frac{1}{n^2}}{\frac{1}{n^2} +1} +\dfrac{\frac{2}{n^2}}{\frac{2}{n^2} +1} + \ldots+ \dfrac{\frac{1}{n}}{\frac{1}{n} + 1}=0$$   but the answer is $\dfrac{1}{2}$ please suggest how to solve this.. thanks. Is expression for law of equipartion of energy valid for real gas? I know that according to law of equipartion of energy ,energy per molecule per degree of freedom is 1/2 Kb T I wanted to know if it is true for a real gas ? .cache/upstart/Unity7.log growing to consume the entire free disk space. Python cypto suspected It's easy to set inline CSS values with javascript. If I want to change the width and I have html like this:  &lt;div style="width: 10px"&gt;&lt;/div&gt;   All I need to do is:  document.getElementById('id').style.width = value;   It will change the inline stylesheet values. Normally this isn't a problem, because the inline style overrides the stylesheet. Example:  &lt;style&gt;    #tId {       width: 50%;    } &lt;/style&gt;  &lt;div id="tId"&gt;&lt;/div&gt;   Using this Javascript:  document.getElementById('tId').style.width = "30%";   I get the following:  &lt;style&gt;    #tId {       width: 50%;    } &lt;/style&gt;  &lt;div id="tId" style="width: 30%";&gt;&lt;/div&gt;   This is a problem, because not only do I not want to change inline values, If I look for the width before I set it, when I have:  &lt;div id="tId"&gt;&lt;/div&gt;   The value returned is Null, so if I have Javascript that needs to know the width of something to do some logic (I increase the width by 1%, not to a specific value), getting back Null when I expect the string "50%" doesn't really work.  So my question: I have values in a CSS style that are not located inline, how can I get these values? How can I modify the style instead of the inline values, given an id? Meta Theory when studying Set Theory What exactly serves as the meta theory in the study of set theory (for example in Kunen's text). It seems to involve a certain amount of number theory and a certain concept of what it means to be finite.   Also: We usually use $\bigcup_{\alpha\in{ON}}R_{\alpha}$ as our set theortic universe $V$ (in the sense we believe that all sets we are interested in live there) where $R_{0}=\emptyset$, $R_{\alpha+1}= \mathcal{P}(R_{\alpha})$ and $R_{\alpha}=\bigcup_{\beta&lt;\alpha}R_{\beta}$ when $\alpha$ is a limit ordinal. The study of independence results then seem to be based on relatavizing notions with this $V$ as our set theoretic universe. It seems that it is implicitly assumed that the $\omega$ in $V$ has no non-standard elemements (in the sense that there is no $n&gt;a$ in $\omega$ where $a$ is obtained be repeatedly applying the successor operation to $0$.) Is this true and can it be formalized or is it something that is taken for granted?   e.g. If the above were true then $ZFC\vdash{\neg{Con(\ulcorner{ZFC}\urcorner)}}$ would imply that $ZFC$ is inconsistent since we may look at the $ZFC$ axioms $\phi_{1},...,\phi_{n}\vdash\neg{Con\ulcorner{ZFC}\urcorner}$, then look at a ctm these axioms (which exists by reflection and downward Lowenheim Skolem) and recover the proof of the contradiction. Summation of natural number set with power of $m$ Who knows about the summation of this series: $$\sum\limits_{i=1}^{n}i^m $$  where $m$ is constant and $m\in \mathbb{N}$?  thanks Add markdown support for hidden-until-you-click text (aka spoilers) 0 ram free on ICS I'm new to the ICS os, coming from Gingerbread from another phone. The phone's quite nice and fast when I first used it, but just this morning it started exhibiting weird actions. Camera360 doesn't open up automatically when I click it, the Camera closes for no reason, Pocket restarts when an article has an image, and TTPod resets the song to the previous song on my widget in the middle of a new song I'm playing.  I checked out the ram, and and was surprised to see 500+ mb used, 0 mb available. I looked at the list of programs and I see the usual culprits like Facebook, but the ram they're using doesn't add up to 500+ mb. Yeah, I know that the whole ram indicated isn't usable by the apps, but I don't think I've done anything to warrant the 0 mb. I close my apps. There are times when there's free 4 to 5 mb, but I think that too shouldn't be the case. I tried installing Advance Task Killer, it listed less than 10 apps, killed it, still the ram is what it is above.   I did a reboot, and now it reads 300+ mb usage, 200 something free.   What can I do? How do I ensure an app's closed on ICS? I installed GoLaucher because it has a handy task killer and I can see the ram freed in an instant, but I would like to know if there's a better way to handle the RAM. If we minimize the Wasserstein loss, $$W_1 (P_S, P_T) = \underset{\gamma \in \Pi}{\text{min }} \sum_{x,y} |x-y|\gamma(x,y)$$ which means we are looking for the coupling $\gamma(x,y)$ that minimizes the cost of moving mass from the source distribution $P_S$ to the target distribution $P_T$,  Do the masses of the source and target distributions have to be identical? If so or not, how are the masses of $P_T$ and $P_S$ accounted for mathematically in, or when minimizing, the shown formula, or what might be missing/overlooked by the Wasserstein approach overall due to the mass differences? Checking for null before event dispatching... thread safe? Are the LIGO observations proof of a black hole merger, and what happened to the black holes? Recent reports claim that the gravitational waves detected by LIGO match up with the signal expected from two black holes merging as predicted by general relativity.  Additionally, the masses of both black holes were estimated. Questions:  How certain are we that the detected of gravitational waves are necessarily from two black holes merging?  Since supermassive black holes are typically at the center of a host galaxy, what happened to the galaxies that contained the two merging black holes?  For example, did their host galaxies merge?    Edit After reading the answers, I understand that the signals detected by LIGO are proof of the validity of gravitational wave generational artifacts as predicted by general relativity.  When additionally gravitational waves, caused by the merger of the supermassive black holes (those which ARE indeed located in the centers of the merging galaxies) will be detected, since mergers of galaxies could be observed by the methods independent of gravitational waves such as registering the fact of the quasar appearance (). Additional questions:  Could someone offer me the historical ASTRONOMY precedent when the second degree of inference (from the mathematical model, being associated with the theory of Physics) was accepted as the discovery of the astronomical object?  Could someone give a reference to trustable scientific publication, with the subject of study being discussion of requirements satisfying claim of astronomical discovery of an astronomical object?  Have independent scientific sources (outside of members of the LIGO team) analyzed methodology and results of the LIGO signal detection, and published their conclusions with regards of what was actually discovered? Erdős-Straus conjecture The  (ESC), states that for every natural number $n \geq 2$, there exists a set of natural numbers $a, b, c$ , such that the following equation is satisfied:  $$\frac{4}{n}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\tag{1}$$  The basic approach to solving this problem outlined by Mordell [Ref1] is described below  By defining $t$ and $m$ as positive integers greater than zero and $q$ a positive integer greater than one we can observe that  a) There is always a solution for even $n$, since if $n=2^qt$ we have the trivial solution $$\frac{4}{4t}=\frac{1}{t}$$  In the remaining case $n=2(2t+1)$, a solution in the form of two Egyptian fractions can always be found  e.g. $$\frac{4}{2(2t+1)}=\frac{2}{2t+1}=\frac{1}{t+1}+\frac{1}{(t+1)(2t+1)}$$  b) If $(1)$ is a solution for some particular prime $n$ then all composite numbers $mn$ divisible by $n$ are also solutions, thus  $$\frac{4}{mn}=\frac{1}{ma}+\frac{1}{mb}+\frac{1}{mc}$$  will also be a solution. This means that we can simplify the analysis to the cases where $n$ is a prime greater than 2.  Using Mordell's approach we have just shown that we only need to consider the cases where $n$ is prime and where $n \equiv 1 \pmod{2} \;\;[meaning \;\;n=2t+1]$  The argument continues...  Mordell goes on to show in turn that the search can be reduced further to the cases when $$n \equiv 1 \pmod{4} \;\;[meaning \;numbers \;\;n=4t+1]$$ $$n \equiv 1 \pmod{8} \;\;[meaning \;numbers \;\;n=8t+1]$$ $$n \equiv 1 \pmod{3} \;\;[meaning \;numbers \;\;n=3t+1]$$ $$n \equiv 1,2,4 \pmod{7} \;\;[meaning \;numbers \;\;n=7t+1,n=7t+2 \;or\;n=7t+4 ]$$ $$n \equiv 1,4 \pmod{5}  \;\;[meaning \;numbers \;\; n=5t+1 \;or\;n=5t+4]$$  Assembling these results together, Mordell showed that the conjecture can be proved in this context except for the cases when $$n \equiv 1,11^2,13^2,17^2,19^2,23^2 \pmod{840}$$  Mordell stated that since the first prime meeting this condition is 1009, this is proof that the conjecture holds for $n&lt;1009$.  This basic approach can be pursued further. Other workers have shown that the conjecture holds for much higher values of $n$ using similar methods as can be seen on the above Wikipedia page.   Note that other intermediate results can be constructed from the above congruence's, e.g. $n \equiv 1 \pmod{24}$.  The question is:  Are there any other elementary approaches to solving this problem than the one outlined by Mordell (and described above)?  [Ref1] Louis J. Mordell (1969) Diophantine Equations, Academic Press, London, pp. 287-290. What is the next perfect square of the form 14444... in decimal notation? We know that $12^2 = 144$ and that $38^2 = 1444$. Are there any other perfect squares in the form of $\frac{13}{9} (10^n - 1) + 1$ (i.e. $1$ followed by $n$ $4$'s), and how would we prove it? Why is the (free) neutron lifetime so long? A neutron outside the nucleus lives for about 15 minutes and decays mainly through weak decays (beta decay). Many other weakly decaying particles decay with lifetimes between $10^{-10}$ and $10^{-12}$ seconds, which is consistent with $\alpha_W \simeq 10^{-6}$.  Why does the neutron lives so much longer than the others?