I've found some camera sensors with very low resolution to use with electronics. Camera have 150x150px and can mount different lenses type: F2.7, F4.0, F6.0.  I want to ask what F means and if I can use this value to found distance at which the object I'm pointing is in focus.
What does f-stop mean? Is it the same thing when people say "2 stops" for example?
How do I select all the columns in a table that only contain NULL values for all the rows?  I'm using MS SQL Server 2005.  I'm trying to find out which columns are not used in the table so I can delete them. Peppers evolved chemicals like capsaicin to discourage animals from eating them, and that chemical itself can cause internal damage if consumed in large quantities, though this is usually only a concern for the hottest of peppers (which people do eat).   Still, why is it that humans seem to be the only animal that often "like" spicy food? Could you list all possible directories where Android apps may store data, providing description what kind of data are stored in each directory? Alternate moves, first one to roll a 6 wins: what's the probability of winning? Does English have any singularia tantum besides mass nouns? How do electromagnetic waves travel in a vacuum? This is perhaps a total newbie question, and I will try to formulate it the best I can, so here it goes. How does an electromagnetic wave travel through for example, the vacuum of space?   I usually see that waves are explained using analogies with water, pieces of rope, the strings of a guitar, etc, but it seems to me that all those waves need a medium to propagate. In fact, from my point of view, in those examples the wave as a "thing" does not exist, it's just the medium that moves (involuntary reference to The Matrix, sorry).   But in space there is no medium, so how does a wave travel? Are there free particles of some sort in this "vacuum" or something? I believe , so supposedly there isn't a medium for the wave to travel through.   Moreover, I've seen other answers that describe light as a perturbation of the electromagnetic field, but isn't the existence of the field, potential until disturbed? How can it travel through something it does not exist until it's disturbed by the traveling light in the first place? (this last sentence is probably a big misconception by me). Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set I'm mainly trying to prove that      If $0\not \in S\subseteq R$ is a multiplicative subset of a   commutative ring $R$ with identity. Then $R-S$ contains a prime ideal.   Now, by using Zorn's lemma, one can show that $R-S$ contains a maximal ideal I. In fact, I is a prime ideal as well, so we need to show this.To do that, I assumed the opposite, i.e $\exists a,b \in R$ s.t $ab\in I$, but $a,b \not \in I$. Then looked each case. However, I stuck when $a,b \in R-[S\cup I]$. The following is what I've done for this case;  Proof:  In this case, our assumptions are $a,b\in R-[S\cup I]$ and $I + (a) = J$, where $J$ is an ideal in $R$ and $J \cap S \not = \emptyset$.   These imply that; $S^{-1}(I + (a)) = S^{-1} J$, but since $J \cap S \not = \emptyset$, by a theorem that we proved in the class, $S^{-1} J = S^{-1}R$.Therefore, it must be true that $\exists (i\in I, r\in R, s_1,s \in S)$ s.t  $$\frac{i+ra}{s_1} =\frac{1}{s}$$ but this implies $\exists s_2 \in S$ s.t  $$ s_2(is + sra -1 s_1) = 0 \quad \Rightarrow \quad (s_1 s )i + (s_1 s r) a = (s_1 s )1,$$ ,so $$(b s_1 s )i + (s_1 s r) ab = (s_1 s )b.$$ Observe that by our assumption $ab\in I$, so $(s_1 s)b \in I$.  Now, at the point, I don't know how to proceed, so I would appreciate any help or hint because I stuck at this point for over a week now.  Edit  Thanks for the great answers; however, but I'm specifically interested in how to continue from the point where I stuck. Factors for max CP at a particular trainer level? Pluralizing abbreviations where the noun is not the last word How to break the Y axis in an Excel sheet I want to break the Y-axis in an Excel sheet. How can I do that?  For example, suppose I have the data in a range from 0-7000 and then range from 22000-28000. I want a break in the Y axis from 8000-20000. How could a statement be true without proof? Godel`s incompleteness theorem states that there may exist true statements which have no proofs in a formal system of particular axioms. Here I have two questions; 1) How can we say that a statement is true without a proof? 2) What has the self reference to do with this? Godel sentence "G" can say that SUB(a,a, no prove) but could be this just arbitrarily judgement about non-provability of "a" because it may simply has a proof which is not yet revealed or discovered? Suppose I know that I can find the $\gcd$ of two integers with the Euclidean algorithm. What is the 'extension' so I can use this method also for polynomials?  Edit: I found an easy answer with less rigor which is approachable without knowledge of matrices:    also the first 3 subchapters of Setup or "set up"? The word setup (as a noun), I feel, has become an acceptable part of the English language, at least insofar as technical manuals or computer textbooks are concerned. However I find that the word is used very often in verb form like so:     "You can setup the program quite easily ..."   when in fact my understanding is that the actual sentence should be:     "You can set up the program quite easily ..."   I would like to know if setup can be used as a verb. The situation seems be very similar to the word output (as a noun). Output is a purely technical word and its use is restricted solely to technical texts or at least in a technical context within non-technical books. However it is also used in verb form now like so:     "The system will output the signal ..."   I would be very grateful if this question is answered. Thank you I keep reading in economics journals about a particular result used in random utility models. One version of the result is: if $\epsilon_i \sim_{iid}, $ Gumbel($\mu, 1), \forall i$, then:   $$E[\max_i(\delta_i + \epsilon_i)] = \mu + \gamma + \ln\left(\sum_i \exp\left\{\delta_i \right\} \right),  $$  where $\gamma \approx 0.52277$ is the Euler-Mascheroni constant.  I've checked that this makes sense using R, and it does.  The CDF for the Gumbel$(\mu, 1)$ distribution is:  $$G(\epsilon_i) = \exp(-\exp(-(\epsilon_i - \mu)))$$  I'm trying to find a proof of this and I've had no success.  I've tried to prove it myself but I can't get past a particular step.   Can anyone point me to a proof of this?  If not, maybe I can post my attempted proof up to where I get stuck. How to get a normal application menu in the top- or titlebar in Gnome Recovering data off of a dead hard drive My hard drive died in my macbook and it no longer will start up. It will not mount in an external enclosure but disk utility is still reading that the hard drive is there, and I tried to repair disk and I am getting this error: (Disk Utility can’t repair this disk. Back up as many of your files as possible, reformat the disk, and restore your backed-up files.) So my question is how do I backup my files if the hard drive won't mount? The only way that I have been able to see the hard drive is through disk utility. I just want to be clear that I am using mac os x snow leapard. What does the helpful flag mean? I don't see "Helpful" in the list of things I can do when I press the flag link.   In my profile page I saw "6 helpful flags."  How do I earn these flags?  May I make them on other peoples' posts or comments?   This is what I am talking about: Origin of the dot and cross product? Most questions usually just relate to what these can be used for, that's fairly obvious to me since I've been programming 3D games/simulations for a while, but I've never really understood the inner workings of them... I could get the cross product equation as a determinant of a carefully-constructed matrix,   but what I want to ask is... How did the dot and cross product come to be? When were they "invented"? Some detailed proofs? Did someone say: "Hey, wouldn't it be nice if we could construct a way to calculate a vector that is perpendicular to two given operands?"  Basically, how/why do they work?  I would appreciate explanations, links to other explanations, other web resources... I've been searching the Internet lately for explanations, but most of them are on how to use it and nothing that really gives substance to it. the output when I start firefox from Terminal I understand that there is an upper limit. But why do you have to type at least 15 characters to post a comment? It is easy to work around it anyway (like adding dots or other useless things).