I've found aphorisms often that play on the meaning of two words and their interaction and was wondering what one might call them.   An example is the PJ Harvey song name:      The whore hustles and the hustler whores.    They are quite simple but interesting.
In this kind of sentence the second half is an inversion of the first half. Is it a rhetorical artífice? What kind?
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$ Suppose that $H$ and $K$ are normal subgroups of a group $G$ such that $HK=G$. I need to show that  $G/(H\cap K)\cong (G/H)\times (G/K)$.  So from the second isomorphism theorem we have that:  $HK/H\cong H/(H\cap K)$ which gives that $G/H\cong H/(H\cap K)$  $HK/K\cong K/(H\cap K)$ which gives that $G/K\cong K/(H\cap K)$  So we must now show that:  $H/(H\cap K)\times K/(H\cap K)\cong G/(H\cap K)$  So consider the map $\theta:H/(H\cap K)\times K/(H\cap K)\rightarrow G/(H\cap K)$ such that $\theta(h(H\cap K)\times k(H\cap K))=hk(H\cap K)$  Now this is a homomorphism and is surjective. To check injectiviy we see that if:  $\theta(h_1(H\cap K)\times k_1(H\cap K))=\theta(h_2(H\cap K)\times k_2(H\cap K))$ then we have that:  $(h_1k_1(H\cap K))=(h_2k_2(H\cap K))$ so that $(h_1k_1)(h_2k_2)^{-1}(H\cap K)=(H\cap K)$ which gives that $h_1k_1(H\cap K)=h_2k_2(H\cap K)$ So we are done.  Is the above correct?  Thanks for any help date command not resolving properly in bash alias I would like to travel in the USA for a period of 3 - 6 months. But I want to spend some time working for my employer (remote work) and getting paid by the employer. Is this possible under a tourist visa (B1/B2)?  I hope this is OK since I will not be getting paid by a US employer. I am in the IT trade so all that I will be needing is my own laptop and a connection to the internet. The money I earn would actually help me pay for the expenses I get during the holiday. Found a similar question , but with some minor differences. Is it archaic to use have you in sentences such as this:     John : I think we can see it with a specially crafted telescope.   Mary : Have you such a telescope?   instead of     Mary : Do you have such a telescope?   Is it still used in official and casual conversations? Do we need to unbind event listeners in directives when angular starts to destroy? In a table, how can I draw a horizontal line that goes only through some of the cells? I mean a line like the one in the Foo and in the Bar area of this table:  +----+-----+ |Foo |1 |2 | |    |1 |2 | |    +--+--+ |    |1 |2 | |    |1 |2 | +----+-----+ |Bar |1 |2 | |    |1 |2 | |    +--+--+ |    |1 |2 | |    |1 |2 | +----+--+--+ Name finding problem with comment notification feature I just received the following in my Response pane (from ), but you can see it was meant for another user.  The @Robert line seems to have found 'Robert' in my name first, instead of Robert C. Cartaino.  I think the comment notification feature should match based on the closest match from the first character in a name (in posting order), and not just the first match found in posting order. Why is $1^{\infty}$ considered to be an indeterminate form From : In calculus and other branches of mathematical analysis, an indeterminate form is an algebraic expression obtained in the context of limits. Limits involving algebraic operations are often performed by replacing subexpressions by their limits; if the expression obtained after this substitution does not give enough information to determine the original limit, it is known as an indeterminate form.    The indeterminate forms include $0^{0},\frac{0}{0},(\infty - \infty),1^{\infty}, \ \text{etc}\cdots$   My question is can anyone give me a nice explanation of why $1^{\infty}$ is considered to be an indeterminate form? Because, i don't see any justification of this fact. I am still perplexed. Who was the piano player that Starbuck met in the bar on Galactica? Towards the end of season four, Starbuck meets a piano player in the makeshift bar on Galactica.  Now, it appears that this guy is some kind of ghost/angel like Caprica-6 and the ghost Baltar - but I have an idea that he could also be the original copy of the seventh model (Daniel). It's mentioned right in the episode before that Cavil poisoned all of the bodies that were being prepared to accept a copy of Daniel - but it's ambiguous about the fate of the original cylon with that personality. Daniel was also mentioned as an 'artist' and 'sensitive' person.  So - could it have been Daniel that helped Starbuck realise what the music meant? Switching from MTB to road handlebars Can PS4 Minecraft join with PC Minecraft? I had to create an 800mm x 2000mm print and so I started by actually creating a 800mm x 2000mm file in Illustrator.  The file contained only vectors so my question is:  Can I create my file size dimensions to be smaller as long as it keeps the correct ratio for the final print?  Like I said, vector ONLY, no photos or raster images. "Above"/"below" before/after a noun Consider two different shaped containers having same area: one is cylinder, the other is like an inverted pyramid (roughly). Both have the same level of water, the weight of the inverted pyramidal container will therefore be greater than that of the cylinder. But I know from Pascal's law that the pressure should be same in both containers. If the base areas are the same then the force (weight as measured by a scale) should also be the same. Why are the weights different? Why did a Dementor try to take Harry's soul in the train? In "Harry Potter and the Prisoner of Azkaban" - when Harry and his friends were travelling to Hogwarts by train, the train stopped in between and Dementors were searching for Sirius Black. Why did one of the Dementors try to take Harry's soul? List of generally believed conjectures which cannot all be true There are some conjectures which most leading experts believe in albeit no one can prove it yet. For example: $\mathcal{P} \neq \mathcal{NP}$, the Riemann hypothesis or the Collatz conjecture.  My question is whether there is a set of such conjectures which cannot all be true, eg. is a statement such as "Either $\mathcal{P} = \mathcal{NP}$ or the Riemann hypothesis is wrong" true? My Mac is getting really slow, what should I do? Why do I get the error "failed unmounting /var" during shutdown? I have a fresh install of Debian 9.0.0. It has a separate 1 GB partition for /var formatted at ext4. When I shutdown from the terminal, using shutdown -h now, there is a bright-red error message stating "failed unmounting /var".  What is the fix for this error? I am trying to construct a theoretical Diffie-Hellman key exchange protocol. However, i cannot understand the difference between choosing an additive group or a multiplicative group. I believe an additive would make it much more simple, but would a multiplicative group make it more difficult to break? What would be the difference between the use of those 2 kinds of number groups? Is there a way to take a mesh, cut it with seams or sharp edges and flatten it, so that the faces stay the same shape and size?  Making paper models is one aspect, where you could use that technique.  No, I'm afraid SZ0Return is not going to do it properly.  And misusing the UV-unwrap is only a last option.    Note, while it's an option to revert to Blender 2.49 which had a script to do this, I'd like a solution that I can use inside the current workspace.