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For some reason, be it some bad habit or something else, I can not understand why the statement "p only if q" would translate into p implies q. For instance, I have the statement "Samir will attend the party only if Kanti will be there." The way I interpret this is, "It is true that Samir will attend the party only if it is true that Kanti will be at the party;" which, in my mind, becomes "If Kanti will be at the party, then Samir will be there."   Can someone convince me of the right way?  EDIT:  I have read them carefully, and probably have done so for over a year. I understand what sufficient conditions and necessary conditions are. I understand the conditional relationship in almost all of its forms, except the form "q only if p." What I do not understand is, why is p the necessary condition and q the sufficient condition. I am not asking, what are the sufficient and necessary conditions, rather, I am asking why. How can I wake-up a PC using a command? (i.e. equivalent to moving a mouse, etc) It doesn't seem like this would be very difficult, but how can I wake-up a PC by doing the equivalent of moving a mouse or pressing keys on a keyboard?  My PC is running Windows 10 and I only have the monitors enter sleep mode after 15 minutes.  The rest of the PC is still awake and doesn't use hibernate, etc.  I'm trying to use EventGhost to receive a TCP/IP command that tells the PC to wake up the displays but it's proving quite difficult. How did Anakin Skywalker survive Order Sixty Six? . When activated, troopers would immediately perceive Jedi as a threat and kill them.  Since Anakin was a Jedi until around the time of the Order, how did the troopers know not to kill Anakin? How many connected components does $\mathrm{GL}_n(\mathbb R)$ have? I would like to see everything on my computer screen in grayscale (like say the kindle screen). How do I do this? I need to periodically run a command that ensures that some text files are kept in Linux mode. Unfortunately dos2unix always modifies the file, which would mess file's and folder's timestamps and cause unnecessary writes.   The script I write is in Bash, so  I'd prefer answers based on Bash. Do electrons move around a circuit? We could imagine a simple electronic circuit composed by a power source and a resistor.   It is usual find descriptions as "The moving charged particles in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom, and can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors." (wikipedia ). That made me imagine electrons going from power -, running by the wires, crossing the resistor and returning to power +, where they suffer a new kick to power -. All that at near the speed of light.  In this model, it is easy to define "electrical current intensity" as proportional to the number of electrons per second that cross one specific point of the circuit.  However, looking for the physics of resistivity, I can read the phrase "The actual drift velocity of electrons is very small, in the order of magnitude of a meter per hour." (wikipedia ). This is a complete different point of view, where electrons are more or less fixed around a fixed position (or moving very slowly), an electricity is a wave of "collisions" or "jumps" of electrons, like in a Newton's cradle (or "do the wave" as public in a football match). Obviously, we do not need severals hours from the switch on to the light on.  So, the question is, do electrons move around a circuit ? References to band theory are welcome.  A related question is: if electrons doesn't moves along the circuit, what is "electrical current intensity"?  Note: I known there are similar questions already posted, but answers of the ones I've read are not very detailed (could be I've not found the best ones). Please, be a few patient before "close vote". "None" as plural indefinite pronoun In my grammar book (English Grammar, HarperCollins Publishers), I read that none is occasionally treated as plural, but it is usually regarded as singular. Can you give me an example of sentence where none is used as plural pronoun? Markov/Chebychev inequality If Z is a square integrable random variable such that $E[Z]&gt;0$, then prove that  $$P(Z\geq k) \geq \frac{(E(Z)-k)^2}{E(Z^2)} \forall k \in [0,E(Z)]. $$  This is a homework question and I don't even understand why the inequality is reversed comparing to Markov/Chebychev inequality. Should Cauchy-Schwartz inequality be used? If yes, then how to begin? Thanks a ton! Blender is rendering an older version my project When app is moved to SD card, where is the app data stored on SD card? Use central limit to solve a problem I am asked to solve the following question using central limit theorem. In an election between two candidates, A and B, one million individuals cast theirvote. Among these, 2000 know candidate A from her election campaign and vote unanimously for her.The remaining 998000 voters are undecided and make their decision independently of each other byflipping a fair coin.Approximate the probability pA that candidate A wins up to 3 significant figures.  It's easy to solve directly. PA = $\frac{0.5(10000-2000)+2000}{10000}$ = 0.501. However, I am quite confused about how to solve this problem by central limit theorem. Java String array: is there a size of method? Say a prospective PhD has a high reply rate (90-95%) to first contact emails with potential superviors. He/She has a well thought out e-mail, but a particular professor (here: USA) that is in the top preferences does not reply after two to three e-mails that were sent within a time frame of three months. I also followed the instructions on the professor personal website in the section "prospective PhD students". The student has already contacted some of the advisor students and has received positive feedback about the professor.  Should the student just give up and move on? Should the student keep trying?  Aside from the obvious "I have too many incoming e-mails to answer" or "I am out in the field", what could create a no response behavior from the professor?  I have seen the simplistic answer "move on, bad advisor, doesn't have time, etc". But this seems a contradiction in this case. The PhD students like the professor and say he/she is personable and no e-mail response after a few well written emails. Let's say it again, we all make mistakes, and I have just made one.  A brief history: I was doing some stuff on a VPS (Debian) I'm renting, when I noticed some strange behaviour. Using the netstat command I saw an non-authorized connection through SSH. I didn't know what to do, so I decided to close his connection using iptables:  iptables -A INPUT -p tcp --dport ssh -s IP -j DROP   But I am tired, and I wrote  iptables -A INPUT -p tcp --dport ssh -j DROP   and I kicked myself (and everyone else) out...  How do I fix this? Using Nouns or Gerunds Could anyone explain when to use a noun or a gerund?  Are these sentences correct? What is the difference between usage of gerund and noun there?        I worked on the improvement of the article.   I worked on the article improving.   I worked on the improving of the article.                The investment idea was published.   Investing idea was published. are the uses of 'bare infinitive' & 'participle' same here? I saw him sing     I saw him singing    In the first example, the verb sing is used as a bare infinitive and in the following one it is exemplified as a present participle. My question is  if both of them are expressing the same meaning? Very new player here. Looking at the stat block of a goblin: for a shortbow attack it says +4 to hit and the goblin has a Dex modifier of +2.   Does this mean I add 6 to the d20 roll or just the 4 and ignore the Dex modifier?  Same with using Stealth. It says Skills: Stealth +6. So would I take 6 and add +2 of the Dex modifier or just add 6 to the d20 of the Stealth check roll?  Thank you! Proving there are infinitely many pairs of square-full consecutive integers So the question goes like this :  A positive integer $n$ is called square-full if for every prime $p$, $p \, | \, n$ implies $p^2 \, | \, n$, i.e. every prime power factor of $n$ occurs at least at the second power. This is equivalent to saying that there is no prime $p$ such that $p \, \| \, n$.  Show that there are infinitely many consecutive pairs of square-full numbers, i.e. infinitely many $n$ such that $n$ and $n+1$ are square-full.  The context of the question highly suggests that this can be proved by induction and it is the solution that I am looking for. It is not a homework, just something that caught my attention because I couldn't find any natural answer to it... I hope I'm not missing something trivial!  I've tried assuming $n_1, n_2, \dots, n_k$ were the first $n_k$ integers such that $n_i$ and $n_i+1$ are square-full, and then generate some polynomial in those $2k$ integers to get a new couple $n_{k+1}$, $n_{k+1} + 1$ but after a few natural tries I got nothing good out of it. Any ideas? How do I pick a part that goes into a breadboard when I order it? I have just bought some 555 timers and they are timers for microelectronic circuits...could anyone tell me what I need to search for in order to get larger ones which will fit a breadboard? Thanks