Would you say  "The different types of cars"  or  "The different types of car"?  In reality my doubt is about types of event/events but can be more confusing to explain what I mean.  I have many events of the different types.
When speaking precisely or technically, one would say that "Homo erectus and homo sapiens are two species of hominid" rather than "Homo erectus and homo sapiens are two species of hominids." The hominid here should be singular because we are speaking about instances of a single class ("class" being used here in its broader sense, not in the sense of taxonomic grouping).  Now let's consider more common parallel constructions replacing the word species with other words.      Tide and Wisk are two brands of detergent.       Tide and Wisk are two brands of detergents.      Cats and dogs are two types of pet you can buy at Pets-R-Us.       Cats and dogs are two types of pets you can buy at Pets-R-Us.   I feel that using the singular noun to specify the class is more grammatically correct, but sounds stilted in conversation. Almost everyone I hear making these constructions uses the plural form. What are your thoughts about singular vs. plural here?  Edit  Here's a more extreme example that may help clarify the issue. Consider the following sentence:     It was my first attempt at calming an angry crowd, and I just        stood there while people were hurling all kinds of insults at me.   Here I think the singular insult sounds strange, if not downright wrong.  Further Edit  I just noticed in A Treasury for Word Lovers (Morton S. Freeman, 1983) a section entitled "Types of Errors." This is a book about (American) English usage by an English professor and editor, which purports to be a "practical guide for serious writers and readers." I wish I could say this discovery satisfies the question, but in fact I now feel somewhat farther from the truth, if there is any single "truth" in this matter. But at least I don't have to worry about being wrong when using the plural form of the class in these constructions.
Primary decomposition of a monomial ideal Compute the moment generating function of $Y = X_1X_2 + X_1X_3 + X_2X_3$ Several files in my home directory have been disappearing. E.g. .bashrc, .bash_profile, authorized_keys and now .profile.  Regardless of how this happened, I would like to restore the original pristine .profile file. If I create a new user on my system one is created. Where can I find this .profile contents from a fresh, untouched install? Speed of light travel When is a gerund supposed to be preceded by a possessive adjective/determiner? "Comments only" lock notice on closed questions mistakenly says that question is still accepting answers When a question has a &quot;comments-only&quot; lock, the following notice is displayed on top of the question:  Locked for X days. Comments on this question have been disabled, but it is still accepting new answers and other interactions.  However, I noticed that if the question is closed (even before the lock), the same notice is used:  ..which could be confusing, especially for new users. Proposed change to the notice on closed questions:  Locked for X days. Comments on this question have been disabled, but it is still accepting [votes and] other interactions.  Or, as others have suggested, the additional &quot;but it is still accepting [...]&quot; part can simply be removed as it hardly provides any new information. This occurs in the  released recently to the public. When someone posts a code block in their question or answer, the code block is cut off on the right hand side, and I can't scroll to the right to view the rest of it. How can I view these code blocks? Can somebody tell me why the counting measure (so, if $S=P(X)$, then $\mu(A)$=infinity if $A$ isn't finite and $\mu(A)=$#$A$ if $A$ is finite) is a measure? (The second property of a measure isn't clear for me). Product of binomial coefficient as a basis Plotting a Continuous signal Current code is:  \begin{enumerate}[label=LEVEL \arabic{*},leftmargin=*]     \item Description of Level 1 \quad L1 \\ \emph{more text}     \item Description of Level 2 \quad L2 \\ \emph{more text}  \end{enumerate}   but the \quad does not align L1 and L2 uniformly vertically. I want to replace \quad with a tab but the tabbing environment does not allow mixing with an enumerate! I am looking for a way to get the output of a command when it is run from within a C++ program.  I have looked at using the system() function, but that will just execute a command. Here's an example of what I'm looking for:  std::string result = system("./some_command");   I need to run an arbitrary command and get its output. I've looked at , but I have not found anything that will give me what I need. How to enable ssh root access on Ubuntu 14.04 I´d like to enable the ssh root access on Ubuntu 14.04. Editing the /etc/ssh_config (PermitRootLogin yes) didn't affect anything. $D_8$ as a derived subgroup Every undergraduate student knows that there are (exactly) two non-abelian groups of order 8: Dihedral ($D_8$) and Quaternion ($Q_8$). The group $Q_8$ has many interesting properties; simple of them are: it has unique element of order $2$, all subgroups are normal, etc. A property, which is strange and not obvious, the group $Q_8$ has, is that there is no group $G$ such that $G/Z(G)$ is isomorphic to $Q_8$. On the other hand, $D_8$ has no such property; there are (infinitely many) groups $G$ such that $G/Z(G)$ is isomorphic to $D_8$; example - $D_{16}$.   The question, I would like to ask, is related to a property of $D_8$, which is not shared by $Q_8$. There are (infinitely many) groups whose derived subgroup is $Q_8$; example- $SL_2(3)$. For groups $G$ of order &lt;100, one can check on GAP that $D_8$ is not a derived subgroup of any group. The natural question is then:  Question 1: Does there exist a finite/infinite group whose derived subgroup is equal to $D_8$?  Question 2: Does there exist a finite/infinite group whose derived subgroup is equal to (general) dihedral group $D_{2n}$ of order $2n$ ($n&gt;2$)? Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$? Using the Fitch system, how do I prove $((p \implies q) \implies p)\implies p$? I started with the hypotheses $(p \implies q) \implies p$ and $\sim p$. However, from these hypotheses I did not get the desired contradiction to solve the question.  Thanks sb45 launch an exe/process with stdin stdout and stderr? In a ring, I was trying to prove that for all $a$, $a0 = 0$.  But I found that this depended on a lemma, that is, for all $a$ and $b$, $a(-b) = -ab = (-a)b$.  I am wondering how to prove these directly from the definition of a ring.  Many thanks! C# Lambda expressions: Why should I use them? I am sure there is something wrong i am doing but i just want someone to point it to me.  Why can't we say that $e^{\frac {\pi i}{3}} = \left(e^{\pi i}\right)^{\frac {1}{3}} = (-1)^{\frac {1}{3}} = -1$ Why do we have to calculate it by the formula as it is (which produces different value)  Another question is why can't we say that $ (-1)^{\frac {1}{2}} = \left(\left (-1\right)^{2}\right)^{\frac {1}{4}} = 1^{\frac {1}{4}} = 1$  Again i have to say that i know this is all wrong i just want to know why it is wrong I try to share my internet connection from my laptop (win7) via virtual wifi to my android phone (Samsung Gio). In an elevated cmd I enter  netsh wlan set hostednetwork mode=allow ssid=VWiFi key=xxx keyUsage=persistent netsh wlan start hostednetwork   The android phone connects to VWifi, but the internet connection is hardly usable on the phone while the internet connection on my laptop is very good at the same time (some Mbps)  What works: I can start WhatsApp, type and receive text messages, so I guess there's no general problem, i.e. config can't be completely wrong - but when I try to send pics or audio or try to receive pics or audio messages then I see from the network monitor on my laptop that the connection doesn't even try to send or receive anything (0 kbps up/down).  What sometimes works: connection to some websites with acceptable speed - but sometimes I don't get a single byte. Also this is not reproducible - the same website sometimes shows up, sometimes android tells my the site was not available.  What never worked so far: connecting to Google Play Store. It always tells me to check my connection and try again.  What I tried so far: I read on problems with IPv6, but no matter if I enable or disable IPv6 in the settings of the virtual Wifi, it doesn't help.  I also read about problems related to static/dynamic IPs, my netsh interface ip show config tells my that dchp isn't enabled on my virtual Wifi connection. If I try to enable it by netsh interface ip set address "myWificonnection" dhcp the android phone won't even connect anymore to the virtual Wifi at all. So there may be a solution here if android would connect with dhcp enabled.  I also read about problems with MAC filters, but this is no router, there's no MAC filter in the virtual Wifi.  When I directly connect to a real WLAN router, everything is fine and working. I have the problems only when trying to get into the internet via the virtual Wifi.  Any ideas what may be configured wrong? Either on laptop or on android? Thanks.