I'm a bit astonished about the long discussions in the post How can I prove a word is a noun? I admit that there a certain problems, especially with gerunds.   Smoking cigarettes is unhealty.   In this example, containing a gerund with an object, it is indeed a bit difficult to say to which word class "smoking" belongs. Is it a noun or a verb?  Traditionally the gerund is seen as a verb form with a double nature. It can behave as a noun and as a verb.  I think it would be practical to see the gerund also as a special word class, a noun-verb thing. In this way we could avoid a lot of problems that arise about the word class noun when we come across gerunds with objects.  My question: Would it be practical to see gerunds as a word class of its own?
I've been studying the Huddleston and Pullum book for four months now. So far only one thing confuses me: the identity of gerund. Is it a noun or a verb?        His constant smoking upset me.  smoking seems  noun because of adjective constant.   Him/His constantly smoking upset me. smoking seems to be verb because of adverb constantly.   Him/His smoking cigars upset me. smoking seems to be a verb because of object cigars.      "His smoking upset me." So is this smoking gerund a noun or verb? Because there is no differentiation, is it both verb and noun? Maybe it's new word category?  Also his seems to be both  sometimes a subject and at other times a possessive determiner. Is that correct?
How do I compute the principal value of a these complex numbers? I have 2 examples I'm not sure how to calculate One being $$\frac{1}{(1+i)^i}$$ the other is $$(-1+i\sqrt{3})^{1+i}$$ Can anyone help please? Anything appreciated I keep hearing about tandem breakers, and how they won't work with 240V loads and how they should never be used for a multi-wire branch circuit.  Aside from those issues...  What is a tandem breaker?     (note: they can be thrown independently). BasicTeX - how to identify packages that need to be added after an upgrade Ambiguity of “not.... because” You are not hired because you are qualified.   I think this means you are hired but it is not because you are qualified. But I think this can  also means you are not hired, and the reason for it is that you are qualified.   Does this ambiguity really exist or do I mistake anything? Cleaning Contaminated Disc Rotors I've had an eternal struggle with my current bike over brake contamination. The levers and calipers are shimano ultegra r8000, so the latest and (almost) greatest.  I first noticed it when I took it to a repair shop (i no longer use) for a bleed, it came back and the front brake would squeal like crazy and at low speeds had little to no braking force. You can stop from speed but then struggle to come to a halt without using your foot.  At around 2000 miles I tried to replace the brake pads, when I took them out they were black with grime on both sets (front &amp; back), not to mention worn down to the metal. I replaced them with the L04C sintered pads, gave the callipers a good cleaning with a towel (no chemicals) and fitted the new set.  Annoyingly all of my braking issues are back, now I probably should have cleaned the rotors, I simply used some muc off disc brake cleaner on them. I would like to know the best way to clean the rotors, I've inspected the pads and they are looking fairly black now, with plenty of tread left. I'm going to abandon these pads and fit a new set. For the rotors I plan to completely remove them from the wheels (they are center lock fitted) and try and treat them off the bike, what is the best way to fully clean them? They have plenty of wear left in them but you can see these black grooves in them, and plenty of muck on the back that I struggle to get off.  Below are images of the rotors after soaking them in disc brake cleaners, waiting and then wiping them down with a clean, microfiber towel.   Front Wheel Outside Rotor   Front Wheel Inside Rotor - note the increased dirt on this side  Looking at ways people clean their disc rotors, I've seen plenty of suggestions that I would need to burn the contaminants off the discs. Would the best approach be to remove them and use a blowtorch, should I soak them in some nasty chemicals overnight before I try to heat them? Do I try baking them in the oven?  And finally, what is the best way to prevent the brakes from becoming contaminated in the future? it's really off putting when they squeal and don't perform how I'd expect because it means I'm more reserved whilst out riding on the bike, leading to reduced time riding around outside. I commute on this bike (50 miles a week) and then ride about 50 on the weekends also, so it see's it's fair share of road use. I tend to wash it once after my big ride on saturdays and will rinse it off if it's been raining, any day that occurs (since I live in north east england, the acid rain..). I've owned disc brake bikes before and never had half the issues I've had with this, I had a cheap trek with tektro brakes and the brakes were sharper and never had any issues with contamination whatsoever (i did around 500 miles on that bike before a motorist happened).  Thanks for any and all advice :) For all infinite cardinals $\kappa, \ (\kappa \times \kappa, <_{cw}) \cong (\kappa, \in).$ I don't understand the proof to the a/m claim. How we know that $\eta &lt; \kappa$ and $(\alpha,\beta)&lt;_{cw} (0, \eta) $ and hence $h: \mu \to \eta \times \eta$ is injective? Appreciate if anyone could advise.  Here is an excerpt of the proof:  For an infinite ordinal $\kappa,$ the canonical well-ordering of $\kappa \times \kappa,$ denoted by $&lt;_{cw}$ is defined as follows: $(\alpha_1, \beta_1)&lt;_{cw} &lt; (\alpha_2, \beta_2)$ iff either one of the following holds.  $(1): \max\{\alpha_1,\beta_1\} &lt; \max\{\alpha_2,\beta_2\}$  $(2): \max\{\alpha_1,\beta_1\} =\max\{\alpha_2,\beta_2\}$ and $\alpha_1&lt;\alpha_2$   $(3): \max\{\alpha_1,\beta_1\} =\max\{\alpha_2,\beta_2\}$ and $\alpha_1 = \alpha_2$ and $\beta_1 &lt; \beta_2.$  Claim: For all infinite cardinals $\kappa, (\kappa \times \kappa, &lt;_{cw}) \cong (\kappa, \in).$  Proof: (It has been show that it is true for $\kappa = \omega$) Assume there is a counterexample  $\kappa.$ Let $A= \{\lambda \in \kappa + 1| \lambda\geq \omega \ is \ a \ cardinal \ and \ (\lambda \times \lambda, &lt;_{cw}) \not\cong (\lambda, \in)\}.$ Then, $\kappa \in A.$ Let $\mu$ be least element of $A.$ Thus, $\mu &gt; \omega$ and for all $\lambda,$ if $\omega \leq \lambda &lt; \mu$ and $\lambda$ is a cardinal, then $(\lambda \times \lambda, &lt;_{cw}) \cong (\lambda, \in).$  By Comparability theorem, $(\mu, \in)$ is isomorphic to initial segment of $(\mu \times \mu, &lt;_{cw})$ since $|\mu \times \mu| \geq \mu$ and $\mu$ is cardinal. Let $(\alpha, \beta) \in \mu \times \mu$ such that $(\mu, \in)$ is isomorphic to initial segment of $(\mu \times \mu, &lt;_{cw})$ given by $(\alpha, \beta).$ Let $h$ be the isomorphism. Let $\eta= \max\{\alpha, \beta\}+ \omega.$ Then $\eta &lt; \kappa$ and $(\alpha,\beta)&lt;_{cw} (0, \eta).$ HENCE, $h: \mu \to \eta \times \eta$ is injective. Consider a set $A$ of $10$ integers, $A = \{a_1,a_2, \ldots ,a_{10}\}$. Prove that there is at least one subset of $A$ whose sum is divisible by $10$. I viewed in this post  a solution to my question, but...    Are there any easier way (or alternative) to do this using colors?  Thank you. ------------------ edited after showed than it´s duplicate ------------- I think that there are many sols, but for example this is easy using a normal table without pgf...     I´m trying to adapt to similar colors to apply to the table probabilitiess What does "upgrade to 18.04" mean? I'm using Ubuntu 16.04 LTS on an Asus K53E laptop with 8 GB RAM. I check for updates to the software daily. If there are no updates, it asks me if I want to upgrade? What does upgrade exactly mean? Will my personal files still be there? Will it wipe EVERYTHING and give me a completely new installation of Ubuntu? Or will it allow me to keep my files and applications, and merely upgrade the OS?  When I upgrade my Mac or Windows machines, my personal files remain available after the upgrade. Does Ubuntu do the same, or are there completely different "rules"? We moved to a new place where the dryer connection is 3-prong instead of 4-prong. The dryer was originally 4-prong, so we bought a 3-prong cord and installed it. It works fine, except I am not entirely sure if I installed the ground wire correctly.   Originally, there was a green wire on the cord itself, and that was connected to the screw on the top of the first picture. This is, I assume, used to ground the case and prevent shocks when touching the exterior of the dryer.  Now with the 3-pronged plug, there is no ground wire on the cord. So where does the existing green wire in the case go? Do I leave it where it originally was like in the first picture or do I connect it to the central terminal like in the second picture?      There's no bonding strap running from the case to any terminal. I can't tell where the green wire is connected to. What could cause a microcontroller to unexpectedly reset? One particularly irritating variety of bug in a microprocessor-controlled system is for the microprocessor to unexpectedly reset. An important tool for debugging this kind of problem is a list of possible causes. What could cause a microcontroller to unexpectedly reset? How to indent subsection in AMS TOC I used AMS LaTeX template with gsm-l package to write my teacher's book.   The table of content that produced has the following form:    in which 1, 2, 3.... are sections and 3.1, 3.2, 4.1, 4.2,.... are the subsection.   I want to indent the subsection with respect to the section, like this (it's ok without dots, though): How can I find my hardware details? Is there any built-in software or terminal method allowing me to view the hardware profiles on my system? Windows equivalent of such a feature would be Device Manager. Proof that $\frac{a^2}{b} + \frac{b^2}{c} + \frac{c^2}{a} \geq a+b+c$ I've tried getting everything on the left side and transforming it into something squared so that I can prove it's bigger or equals to 0 but I've been unsuccessful. Would depositing large cash amounts cause problems? I saw  recently where a man withdrew $600,000 USD in cash from his bank.  I'm sure many folks here would advise against this move for obvious (and perhaps not-so-obvious) reasons.   My question: suppose you did this and then, some months later, changed your mind and wanted to re-deposit with a bank.  I assume the gent cannot simply walk into a bank with $600,000 USD and deposit it, right?  Wouldn't money-laundering alarms be raised?  Wouldn't the IRS like to know where the money came from? The Mac editor Latexian has built in methods for compiling using latex+dvips, pdflatex and xelatex.  Furthermore, it assumes bibtex and makeindex to deal with bibliographies and indexes, respectively.  How do I customize Latexian to use, e.g. LuaTeX for compiling or Biber for bibliographies? When looking at a PDF document I often want to zoom-out to scroll quickly to its contents and get an overview.  However, when I zoom-out past a certain threshold (it seems to differ per PDF) Safari thinks I want to see the tab overview:    I have never found a use for this function, so it only causes annoyance.  Can I turn this tab overview off somehow? A solution that uncouples the pinch-to-zoom gesture from the functionality would also work.  I'm on Mountain Lion 10.8.5 with Safari 6.1.3. What should I do when the GETDEB repository is down? Fullscreen Vista's Command Prompt, or Replacement Opening the command prompt ("cmd") on Vista into full screen causes the application to take up 100% vertical space, but only about 50% horizontal. Is there not a way I can make this fullscreen? If it's simply not possible, what is a good replacement? I read a comment under :     There are plenty of events that can occur that have zero probability.   This reminds me that I have seen similar saying before elsewhere, and have never been able to make sense out of it. So I was wondering    if zero probability and impossibility mean the same? if an event with zero probability doesn't mean that the event is impossible to occur, how probability theory represents/describes impossibility?   Thanks and regards!