why is PI considered irrational if it can be expressed as ratio of circumference to diameter?
Why is $\pi$ irrational if it is represented as $C/D$?
Here is the top output which I gathered:    I noticed that top is showing vlc's cpu usage is > 100%.  Can anybody please justify me why it is showing like this, whether this is a bug in top application or something else. "Each of these is" vs. "each of these are" Each of these CDFIs are finding solutions for communities that lack   access to traditional financial products and services, and the NEXT   Awards will accelerate their success.   OR     Each of these CDFIs is finding solutions for communities that lack   access to traditional financial products and services, and the NEXT   Awards will accelerate their success.   The difference is, the first one uses "CDFIs are" and the 2nd sentence uses "CDFIs is"  Which one is correct? Any why? Solving $4x = e^x$ without graphing and looking for intersection Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions Exercise: Define a polynomial $\Sigma(X_1,\ldots,X_n)$ as \begin{align*} \Sigma(X_1,\ldots,X_n) = \prod_{i &lt; j} (X_i+X_j) \end{align*} This is a symmetric polynomial, quite clearly. I want to express $\Sigma$ as a polynomial in the elementary symmetric functions, for $n=2,3,4$. Case $n=2$ is trivial: $\Sigma(X_1,X_2)= \sigma_1 = X_1+X_2$. Case $n=3$ is easy. I write $\Sigma$ as follows: \begin{align*} \Sigma(X_1,X_2,X_3) = (\sigma_1 - X_1)(\sigma_1 - X_2)(\sigma_1 - X_3), \end{align*} then apply  formally, obtaining \begin{align*} \Sigma(X_1,X_2,X_3) = \sigma_1^3 - \sigma_1 \sigma_1^2 + \sigma_2 \sigma_1 - \sigma_3 = \sigma_2 \sigma_1 - \sigma_3. \end{align*} The case $n=4$ seems harder to me, and I'm unable to work it out. I hope there is some trick to avoid unnecessary computations. My attempt is to write down $\Sigma$ completely: \begin{align*} \Sigma = (X_1+X_2)(X_3+X_4)(X_1+X_4)(X_2+X_3)(X_2+X_4)(X_1+X_3) \end{align*} and then multiply factors in groups of two, obtaining: \begin{align*} \Sigma = (\sigma_2 - X_1X_2-X_3X_4)(\sigma_2 - X_1X_4 - X_2X_3)(\sigma_2 - X_2X_4-X_1X_3), \end{align*} but it doesn't seem to help much. How can I solve the exercise? prominently sports purple hair.    Is this her natural hair color?  Natural extensions in the answer depending on the correct answer: Is she wholly human and humans in the Galaxy Far Far Away can have this hair color?   Or is she partly human or not human?   Or does she dye her hair?   Or is there another hair color changing technology? High contrast theme and Firefox-Font colour issues? Singular to plural noun Many nouns that end in ‑f are made plural by changing the ‑f to ‑v‑ and adding ‑es.  +----------+-----------+ | Singular |   Plural  | +----------+-----------+ |  half    |  halves   | |  leaf    |  leaves   | |  shelf   |  shelves  | +----------+-----------+     But some nouns that end in ‑f are made plural simply by adding ‑s.  +----------+-----------+ | Singular |   Plural  | +----------+-----------+ |  chief   |  chiefs   | |  roof    |  roofs    | |  cliff   |  cliffs   | +----------+-----------+   Some nouns that end in ‑f can be made plural in two ways, either by adding ‑s or ‑ves:   +----------+--------------------+ | Singular |      Plural        | +----------+--------------------+ |  scarf   |  scarfs or scarves | |  hoof    |  hoofs or hooves   | |  dwarf   |  dwarfs or dwarves | |  wharf   |  wharfs or wharves | +----------+--------------------+   Now my question is how to determine whether to use only ‑s or to change the ‑f to ‑v‑ and add ‑es? Showing that $\displaystyle\lim_{s \to{1+}}{(s-1)\zeta(s)}=1$ I need prove the following: ($\zeta(s)$ is the Riemann zeta function)  $\displaystyle\lim_{s \to{1+}}{(s-1)\zeta(s)}=1$  I really don't know, I have tried hard, but have obtained nothing for now. Do you gain current HP when you level up? Looking for book: contact with aliens, five different races, mismatched claws, biological imperative to breed can't create a jobs user profile I'm stuck on this page even after linking stackoverflow and github accounts. How to place text above the figure/table How to place text above the rotated Figure (LANDSCAPE) in the same page. I tried but text automatically moved to the following page.  TEXT TEXT....   \begin{landscape} \begin{table}[] \centering \includegraphics[width=160mm]{figures2/comparation3.png} \caption{A comparison of Aloha protocols} \label{tab:ComparationAloha} \end{table} \end{landscape}     I added this code, but one part of table disappeared. I must have type TABLE since I need it for list of tables later.  \lipsum[11] \begin{table}[h!] \rotatebox{90}{\parbox{100mm}{ \includegraphics[width=160mm, rotate=90]{figures2/comparation3.png} \caption{A comparison of Aloha protocols} \label{tab:ComparationAloha}}} \end{table} \lipsum[12] What is the difference between # and . when declaring a set of styles for an element and what are the semantics that come into play when deciding which one to use? I have a production server running with the following flag: -XX:+HeapDumpOnOutOfMemoryError  Last night it generated a java-38942.hprof file when our server encountered a heap error. It turns out that the developers of the system knew of the flag but no way to get any useful information from it.  Any ideas? A potential customer wants to evaluate our storage system. They run Windows 2008R2 x64 with 4KB NTFS on a virtual test machine they've sent us. They did not seem to know this at hand, so I think it's reasonable to assume that environment was not tweaked. The tests are inserting, indexing, searching, deleting. Tool is not known to me.  Given that the windows NTFS block size is 4KB, and SQL write in 64KB chunks - is it safe to assume that a block size of 64k on the SAN is a good choice?  They run SQL Server 2008, perhaps standard. What can cause "Discovered - currently not indexed" in the new GWT "Eat" is to "feed" as "drink" is to what? I can say "I feed someone". Am I forced to say "I give someone a drink", or is there a single word for this (as in "I [verb] someone")?  Unfortunately my thesaurus can't really help me. Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$ How configure the DHCP settings of WIFI Tethering (Hotspot) on Android? When connecting my PC to Android Wi-Fi hotspot, it assigned a 192.168.42.x address to my PC. I really need to change this as it conflicts with one of our work subnets - is this possible? A situation came up in my session where a fighter used his Shield Master Shove feature to shove a Giant Crocodile that was currently restraining another PC using it's bite+grapple ability.  I did a quick check at the time and did not find anything related to shove, although in the  condition description it states:     The condition also ends if an effect removes the grappled creature from the reach of the grappler or grappling effect, such as when a creature is hurled away by the thunderwave spell.   I ruled at the time that a shove would count in a similar way to being "hurled away" however I wasn't sure and said I would find more concrete information for the future.  I have searched high and low for somebody else asking this specific question but have yet to find it. I saw some reference to a Jeremy Crawford tweet about involuntary movement and grappling however I am unable to find it.  If a third party "shoves" a creature that is grappling another, does it only shove the grappler away, or does it move both the grappler and grappled?  I drew a diagram:   (; this question relates to if a third party shoves the grappler instead, so it's not a duplicate.)