None of the 26 answers given , or the 5 answers given  mentions any similarity between the pronunciation of  E = mc² and  A = πr², yet I still remain confusioned as to what distinguishes the reading of E = (mc)² and A = (πr)² with the reading of the first two.
123807
According to one of the questions  on EL&amp;U, “E = mc²” is read as     E equals M C squared.   How do we read “E = (mc)²” so that it is not mistaken for “E = mc²”?
80766
I read this sometime ago,     Aoccdrnig to a rscheearch at   Cmabridge uinervtisy, it deosn't mttaer   in waht oredr the ltteers in a wrod   are, the olny iprmoetnt tihng is taht   frist and lsat ltteer is at the rghit   pclae. The rset can be a toatl mses   and you can sitll raed it wouthit   porbelm. Tihs is bcuseae we do not   raed ervey lteter by it slef but the   wrod as a wlohe.   I'm guessing that the Cambridge research probably doesn't exist, but is it true that we can normally understand a sentence whose letters are scrambled in this way?
92931
In my class, there is no distinction made between,   $$ C_{ab}{}^{b} $$ and  $$ C^{b}{}_{ab}. $$ All I know, and read about so far, is the distinction of covariant and contravariant, form/vector, etc. etc. But what is this slanted business all about?
85857
I tried the following $$I = \langle X^2,X+1\rangle =\langle X^2,X+1,X^2+2(X+1)\rangle =\langle X^2,X+1,(X+1)^2+1 \rangle$$  Yet no matter how I arrange it, I cannot obtain $1$. Can someone help me out?
98951
There are so many available bases. Why is the strange number $e$ preferred over all else?  Of course one could integrate $\frac{1}x$ and see this. But is there more to the story?
48304
I've tried both calculations on Wolfram Alpha and it returns different results, but I can't get a grasp of why it is like that. From my point of view, both calculations should be the same, as $2.5=25/10,$ and $(-2)^{2.5}$ is equal to $(-2)^{25/10},$ relying on a general rule $(a^m)^n=a^{mn}$.  Links to sources:
115128
In Peskin and Schroeder's Quantum Field Theory, there is an identity of Pauli matrices which is connected to the Fierz identity, (equation 3.77) $$(\sigma^{\mu})_{\alpha\beta}(\sigma_\mu)_{\gamma\delta}=2\epsilon_{\alpha\gamma}\epsilon_{\beta\delta}.\tag{3.77}$$ The author explains that      One can understand the identity by noting that the indices $\alpha,\gamma$ transform in the Lorentz representation of $\Psi_{L}$, while $\beta,\delta$ transform in the separate representation of $\Psi_{R}$, and the whole quantity must be a Lorentz invariant.   How can one see $\alpha,\gamma$ and $\beta,\delta$ transform in different representation?
114543
I am trying to understand . As far as I could find there are three equivalent definitions and in general many sources start from a different one, still I fail to see their equivalence. I restate the definitions and their equivalences given in the Wikipedia page:   Eigenstate of annihilation operator: $$a|\alpha \rangle =\alpha|\alpha \rangle$$ Displacement operator of the vacuum: $$ |\alpha \rangle =e^{\alpha a^{\dagger}-\alpha^{*} a}|0 \rangle $$ State of minimal Uncertainty: $$ \Delta X= \Delta P = \frac{1}{\sqrt{2}} $$   I fail to see how they are the same! Can someone please explain how to derive these from one another?
48218
Is there any way to easily memorize these? Such as $\sin \frac{\pi}{6} = 1/2$. Any help needed!!!
11805
If one sings the letter "A" and "M" at the same volume and pitch, the two letters are still differentiable. If both pitch and volume are the same however, shouldn't the sound be the exact same?
22585
Take a look at this here:  \documentclass[10pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \begin{document} \begin{align*} \Leftrightarrow \qquad P'_1(t)+\lambda P_1(t)&amp;=\lambda e^{-\lambda t} &amp;&amp; (2.6)\\ \Leftrightarrow \qquad e^{\lambda t}P'_1(t)+\lambda e^{\lambda t}P_1(t)&amp;=\lambda e^{\lambda t} e^{-\lambda t}=\lambda \\ \end{align*} \end{document}   Is it possible to have the equivalences below each other like the equations are?  \documentclass[10pt,a4paper]{article} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \begin{document} \begin{alignat*}{4} P'_1(t)&amp;=-\lambda P_1(t)+\lambda P_0(t)\\ \Leftrightarrow &amp;&amp;\qquad  P'_1(t)+\lambda P_1(t)&amp;=\lambda e^{-\lambda t} &amp;&amp; (2.6)\\ \Leftrightarrow &amp;&amp;  e^{\lambda t}P'_1(t)+\lambda e^{\lambda t}P_1(t)&amp;=\lambda e^{\lambda t} e^{-\lambda t}=\lambda \\ \end{alignat*} \end{document}   This almost works but i have the mention problem that the first line is pulled to the very left.
89862
Is $\aleph_0^{\aleph_0}=2^{\aleph_0}$ or $\aleph_0^{\aleph_0}&gt;2^{\aleph_0}$ Why?
74532
I am confused about something: \begin{eqnarray}     (e^{2 i \pi})^{0.5} = (e^{2 i \pi \cdot 0.5})= e^{i \pi}=-1 \end{eqnarray} but \begin{eqnarray}      e^{2 i \pi}=1~ and~ 1^{0.5}=1  \end{eqnarray} where is my mistake??  thanks
38899
I have two simple questions:   From where do the names  come from? I don't see any intuition between those names in context of order theory. From where does the notation come? I have to admit, I always had an impression that notation we use is somewhat backwards... just take the look at the picture at the wikipedia!    I used this notation a lot of times and I have to admit that often I have to stop for a minute and convince myself that I'm indeed using it right. I'm hoping that learning a bit about origin and context of name choice and notation will make it easier.
93368
For context, this equation is used in the following (from Schwartz's QFT 3.44)  $$\partial_{\mu} \frac{\partial(\partial_{\beta}A_{\gamma})^2}{\partial(\partial_{\mu}A_{\nu})} = \partial_{\mu}\left[2(\partial_{\alpha}A_{\alpha})\frac{\partial(\partial_{\beta}A_{\gamma})}{\partial(\partial_{\mu}A_{\nu})} g_{\beta\gamma}\right] = \partial_{\mu}[2(\partial_{\alpha}A_{\alpha})g_{\beta\mu}g_{\gamma\nu}g_{\beta\gamma}]=2\partial_{\nu}(\partial_{\alpha}A_{\alpha}).\tag{3.44}$$  But doesn't $$\frac{\partial(\partial_{\beta}A_{\gamma})}{\partial(\partial_{\mu}A_{\nu})} = g_{\beta\mu}g_{\gamma\nu}$$ imply, for instance, that  $$\frac{\partial(\partial_0 A_3)}{\partial(\partial_0 A_3)} = g_{00}g_{33} = -1$$ instead of $=1$? Shouldn't we instead have $\frac{\partial(\partial_{\beta}A_{\gamma})}{\partial(\partial_{\mu}A_{\nu})} = \delta_{\beta\mu}\delta_{\gamma\nu}$?
113458
Using the equivalency, I got the answer equal to $1$, however the answer is given as $\frac34$.    also gives $\frac34$.  Could someone tell me that the given answer is wrong or I made a mistake!
48135
I'm attempting to acquire an intuitive understanding of why the content in the question of the title is correct, however I am unable to do so. Is there way of thinking about the result that makes sense?