Punctuation: We promise [that] it's a big deal
Are there rules about using "that" to join two clauses?
How to change the date format? Presently the date is showing as mmm dd hh:mm:ss. Is there any way that I can change it to as per my liking. For example : dd mmm, hh:mm:ss. I am in trouble with polarization and entanglement. Let's consider three cases : Case 1) : Statistical mixture of $|H\rangle$ and $|V\rangle$ polarized photons Case 2) : Photons in a superposition state $1/\sqrt{2}(|H\rangle+|V\rangle)$ Case 3) : Photons which are entangled with twin ones in $1/\sqrt{2}(|H,H\rangle+|V,V\rangle)$ state Which experiments can be conducted to differentiate the case  statistical mixture from the case  superposition state ?   Which experiments can be conducted to differentiate the case  statistical mixture from the case  entangled photons in superposition state ?   Using a $45^\circ$ polarizer I think you can differentiate case 1/case 2 but not case 1/case 3 I don't know how to differentiate case 1/case 3 except maybe using quantic tomography and Wigner function. Is it true ? Is there any other simpler way ? Thanks a lot for your answer and sorry for this maybe dummy question... prominently sports purple hair.    Is this her natural hair color?  Natural extensions in the answer depending on the correct answer: Is she wholly human and humans in the Galaxy Far Far Away can have this hair color?   Or is she partly human or not human?   Or does she dye her hair?   Or is there another hair color changing technology? How much willpower do gravely wounded soldiers lose? The text says they suffer a permanent reduction? Preview on the right please, optionally? On the nilpotence of the matrix $AB-BA$ The level 4 spell Polymorph requires concentration to maintain.  The subject retains their personality and alignment, but they have the mental statistics of the new form, which must be a beast and cannot speak or cast spells.  If a caster targets themselves with this spell, can they concentrate to maintain it, or does this depend on the mental statistics of the beast form they choose?  This situation certainly occurs in practice, since Wizards reaching level 10 in the School of Transmutation gain the Shapechanger feature.  This allows them to cast Polymorph, but only upon themselves and only to change into a beast of CR 1 or lower.  Beasts with CR 1 or less range in Intelligence from the Giant Eagle (Int 8) to the Frog (Int 1). Custom URL Hack - anybody know how can i find the fields IDs from "User" object? I'm new in custom URL hacking.  I am trying to write a custom URL in a custom button. It is suppose to clone the User record, and while doing so, I want some user fields to be cleared. However, I need help identifying those fields IDs (e.g. Email, Name, etc).  How can i refer these fields when writing the custom URL code? How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)? In this current  the following is being proposed:      Suppose you randomly divide 500 million in income among 10,000   people. There's only one way to give everyone an equal, 50,000 share.   So if you're doling out earnings randomly, equality is extremely   unlikely. But there are countless ways to give a few people a lot of   cash and many people a little or nothing. In fact, given all the ways   you could divvy out income, most of them produce an exponential   distribution of income.   I have done this with the following R code which seems to reaffirm the result:  library(MASS)  w &lt;- 500000000 #wealth p &lt;- 10000 #people  d &lt;- diff(c(0,sort(runif(p-1,max=w)),w)) #wealth-distribution h &lt;- hist(d, col="red", main="Exponential decline", freq = FALSE, breaks = 45, xlim = c(0, quantile(d, 0.99)))  fit &lt;- fitdistr(d,"exponential") curve(dexp(x, rate = fit$estimate), col = "black", type="p", pch=16, add = TRUE)     My question How can I analytically prove that the resulting distribution is indeed exponential?  Addendum Thank you for your answers and comments. I have thought about the problem and came up with the following intuitive reasoning. Basically the following happens (Beware: oversimplification ahead): You kind of go along the amount and toss a (biased) coin. Every time you get e.g. heads you divide the amount. You distribute the resulting partitions. In the discrete case the coin tossing follows a binomial distribution, the partitions are geometrically distributed. The continuous analogues are the poisson distribution and the exponential distribution respectively! (By the same reasoning it also becomes intuitively clear why the geometrical and the exponential distribution have the property of memorylessness - because the coin doesn't have a memory either). How do I delete Windows.old in Windows? Why can one bend glass fibers without breaking it, whereas glasses one comes across in real life is usually solid?  Is there also a good high-school level explanation of this? How to apply a macro to each column of a table If a ring element is right-invertible, but not left-invertible, then it has infinitely many right-inverses. I use a 7805 for a project where the circuit needs a higher current (~2.8&nbsp;A) at 5&nbsp;V. So I assume that if I use both ICs in parallel I can increase the maximum current capacity. Would it work? Illogical twoside margins Shouldn't the twoside option produce a wider margin at the binding/spine edge, rather than the other way around? I'm using \documentclass[twoside]{report}. Graphing the amount of time a function takes Always wanting more , of anything, never has enough,never contented with what they have How to carry cologne bottles in hand luggage and prevent losses? So far, I know the matrices $$S=\left( \begin{matrix} 0&amp;-1\\ 1&amp;0 \end{matrix} \right), \quad T=\left( \begin{matrix} 1&amp;1\\ 0&amp;1 \end{matrix} \right) $$ generate SL$(2,\mathbb{Z})$. $S^2=(ST)^3=-I$. I also know the matrices $$X=\left( \begin{matrix} 1&amp;1\\ 1&amp;2 \end{matrix} \right), \quad Y=\left( \begin{matrix} 2&amp;1\\ 1&amp;1 \end{matrix} \right) $$ with their inverses $X^{-1},Y^{-1}$ generate SL$(2,\mathbb{Z})'$, the commutator subgroup. I'm interested in what the quotient $SL(2,\mathbb{Z})/SL(2,\mathbb{Z})'$ is. In general, how would I go about computing the quotient of two matrix groups? I'm trying to use GAP but I'm having a lot of trouble! Prove/Disprove that if two sets have the same power set then they are the same set I am really sure that if two sets have the same power set, then they are the same set. I just am wondering how does one exactly go about proving/showing this?  I'm usually wrong, so if anyone can show me an example where this fails, I'd like that too.  The homework just asks for true/false, but I'm wanting to show it if possible. My thoughts are that since the power set is by definition the set of all subsets of a set, if each of the two power sets are identical, we have an identity map between each set, thus it's indistinguishable which power set is a given set's power set. I hope that wasn't verbose. Since a set has only one power set, we can conclude they are in fact the same set.