Which sentence is correct? Help laughing or help but laugh
"Can’t help but" vs. "can help but"
I'm working on the question     Let $G$ be the group of invertible real matrices of the form $\left [\begin{array}{c c}a &amp; b\\ &amp; a^2\end{array}\right ]$. Determine the Lie algebra $L$ of $G$, and compute the bracket on $L$.   I'm familiar with how to derive the Lie algebra for a linear group like $U_n$, $SU_n$, etc. but I'm not sure what to do in a more explicit case like this. How do I install the Firefox Developer Edition? Is there a website with historical temperatures and weather data? I am interested in hiking this fall in France and camping along the way. In order to figure what gear I need to pack to camp (particularly for the sleeping bag), I would like to know what temperatures to expect.  I am interested in historical temperatures to figure the usual temperature and I might look at them for other seasons. If that matters, I am thinking about hiking in the Pays Basque (South West of France), the mountainous part.  Where (ideally online and for free) can I find such data? Are there resources that cover Europe, or even the whole world? Calculating lat/lons from PostGIS table which has projected coordinate system? I have a PostGIS table in a projected coordinate system (EPSG: 28355 or MGA94 Zone 55). In QGIS (with the PostGIS manager plugin) I calculate a coordinate by performing the following SQL:  UPDATE gisprod.buildings SET easting = x(centroid(the_geom))    Now I want to add a "lat" and "lon" field to this table and calculate the values using the appropriate coordinate system, in this case that would be (EPSG:4283 or GDA94).   Is there a way I can specify in the SQL statement to calculate the x/y coord using a different coordinate system? Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$. Here is my proof, I would appreciate it if someone could critique it for me:  To prove this statement true, we must proof that the two conditional statements ("If $\mathcal{P}(A)⊆ \mathcal{P}(B)$, then $A⊆B$," and, If $A⊆B$, then $\mathcal{P}(A)⊆ \mathcal{P}(B)$) are true.    Contrapositive of the first statement: If $A \nsubseteq B$, then $\mathcal{P}(A) \nsubseteq \mathcal{P}(B)$  If $A \nsubseteq B$, then there must be some element in $A$, call it $x$, that is not in $B$: $x \in A$, and $x \notin B$. Since $x \in A$, then $\{x\} \in \mathcal{P}(A)$; moreover, since $x \notin B$, then $\{x\} \notin \mathcal{P}(B)$, which proves that, if $A \nsubseteq B$, then $\mathcal{P}(A) \nsubseteq \mathcal{P}(B)$. By proving the contrapositive true, the original proposition must be true.    To prove the second statement true, I would implement nearly the same argument, so that isn't necessary to write. So, does this proof seem correct? Also, was the contrapositive necessary? Or is there another way to prove the initial statement? Are there idioms or expressions in English that describe going from one bad situation to one that's even worse?  I heard "between a rock and hard place" but this describes a dilemma not really a transition. I am looking for an expression that describes someone trying to get out of a bad situation but after much effort, the situation only got worse. Let $m$ and $n$ be two integers. Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.   I think I have to use the contrapositive to solve this. So I assume $\neg P\implies Q$ and I have to derive $\neg Q$? I know its easier to show odd numbers rather than even... but im still unsure how to do this practice problem. How and when does the tracking of shared links work? ID a book about a mirror world and 4th dimension I read a book about 10-15 years ago about a boy and a girl who find a mirror. What made the mirror special was, they were able to enter the reflection and be a part of the reverse image world. They end up going to school and when asked to write something on the board, it ends up being backwards, but to them looks normal.  Later, the two end up in a world with 4 dimensions. With the added dimension they can't see as they normally could. If one moved a certain way the other would see their insides. Eventually a native of that dimension made some type of device that lets them see regularly.  Other than that my memory is blank. If I remember anything else I will be sure to edit it in. Recommended visualization libraries for standalone applications delegate keyword vs. lambda notation Once it is compiled, is there a difference between:  delegate { x = 0; }   and  () =&gt; { x = 0 }   ? Why do some adjectives follow the nouns they modify? Right now I can only think of one instance in which this regularly occurs.  The adjective proper is sometimes placed after the noun it modifies, e.g:      A class of cold-blooded oviparous or ovoviviparous vertebrated animals whose skin is covered with scales or scutes; the reptiles proper.   What is this word order called, and why is it ever used?  Edit: I really want to know about proper, and while the word hyperbaton relates to post-positivity when it is meant to be rhetorically impacting, it doesn't seem to fit with ubiquitous post-positivity, such as that of proper.  I've accepted hyperbaton as the correct term/reason for almost all post-positive constructions, but I'd like a complete answer to include proper. What is the logic behind the timer of the Sojourner Badge? How to restore file copy / transfer status window? Strange set notation (a set as a power of 2)? I am not very well versed on set theory or syntax, but I thought I knew the basics.  However, in a book about databases I am reading now, the author uses $2^x$ to signify "a set of $x$."  For example, $2^{\text{dogs}}$ is a set of $\text {dogs}$, etc.    The author never really explained this or why he does it, I just picked up the meaning from context.    I am not sure why the exponent operator is used, nor am I sure what the number $2$ has to do with it.  The sets being represented are NOT powers of $2$ (in size)... they come in all sizes.  Is this a valid notation?  I have not seen it anywhere before... I just watched Planet Hulk. At the end the Hulk ends up with someone seemingly almost as powerful as he is. Are the Hulks (Green, Red, and She-Hulk) able to have children? I agree that every page in a site should have a unique TITLE, and that every page should have one and only one H1 element, but should the text of each H1 be completely unique too?  Instinctively one would think so, but there are potentially many cases where (IMHO) mind this doesn't make sense and attempting to do so will impair the user experience &amp; presentation of the page - for example, where pages are part of a closely related cluster, e.g. a multi-step process/tool/wizard.  Surely the process name should go in the H1 (e.g. "Pregnancy Planner"), and the current step you're on should be marked up as a H2 (e.g. "Step 1 - Trying for a baby"), rather than shoehorning both into a single H1 together (e.g. "Pregnancy Planner - Step 1 - Trying for a baby")?  Not only does this make the H1 rather long and potentially impact the presentation of the page, I would argue that in combining both into one you also lose semantic goodness, as the page is surely semantically richer by keeping parent (process) and child (step) as separate, nested headings?  Furthermore, the current proposal I have read is that on the first page the H1 should be the name of the process and the first step an H2, but on subsequent pages the same text should not be a H1 at all (just text styled exactly the same as an H1) and the current step should become the H1 instead. For me this is introducing unnecessary complexity to the page authoring/production process, and inconsistency in the semantic structure of the pages within the stepped process.  So it all comes back to the basic assertion that each H1 must be completely unique, which I question. Can you convince me that this should be so and that the cost/complexity of implementing this (especially in situations such as that above) is worth it?  Your thoughts please... Does deleting iCloud photos affect them on devices? If I delete a photo from my iCloud will it also be removed from my devices that are connected to my account? What do the numbers in a man page mean? Is there a nice solution to get a "presenter mode" for Latex presentations? I really like the way Keynote and MS Office (and also OpenOffice &amp; similar) support a presentation mode that displays the current slide, the next (and maybe previous) slide, the elapsed and current time, and also any notes attached to the slides on one screen and the presentation itself on the beamer/second screen.  It enables me to give good, professional presentations without having to know everything by heart (I suck at that).  I found a , but I am looking for alternatives, especially OS-independent would be great. Not having to create 3 different PDFs is a boon.  Any hints?