Or: how do statements follow from other statements?  Consider:  All turtles have shells (s1), Ricardo is a turtle (s2), therefore Ricardo has a shell (s3).  Why does s3 follow?
I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be .  Consider: :     P therefore Q  P            Therefore, Q   My question is could we have arbitrarily defined it such as:     P therefore Q  P            Therefore, P   However, if an advanced civilization receives information in the form of following nested structures/containers or packets, how will they interpret Modus Ponens if in an alien land Modus Ponens is not defined?    Therefore, it raises the validity of MP. How do we define the implication or entailment operator? Because if we use an argument that relies on implication or entailment operator ipso facto, then it is trivial that logic is circular.  Is there a flaw in my rationale?
How do you join or create a server in multiplayer? I just got Minecraft Pocket Edition on my iPhone, but I'm having trouble figuring out how to start multiplayer. When I go to menu, there is only one button that says Play. How do I join or create servers? How to create an index map of atlas features in QGIS 3? I realise that this question has been asked before (), however I am still unable to figure out how to create an index map of atlas features in the QGIS map composer.  Basically, I have a line and I have five atlas maps showing the extent of the line, and to show where which map corresponds to the line a I need five overviews on a map with numbers on them, which will look similar to below:    I've created five overviews, but as all of these must be set to correspond to the main map frame, all of them show the overview for which ever atlas feature is selected at the time, rather than appearing as separate index tiles.  Can anyone tell me where I am going wrong? Prove that $x^{2} \equiv -1 \pmod p$ has no solutions if prime $p \equiv 3 \pmod 4$. Customize Ubuntu for a library Internet kiosk Wrapping a mesh around point cloud with cavities $$\sum_{k=1}^{\infty} \frac{1}{k^{\ln k}}.$$  I have some problems with this sum, I have tried most of the common methods, such as the ratio/root test, integral test, etc. I do believe it looks like a problem easily solvable by a direct comparison with some p-series, however, I do not know how to formulate the inequality.   I did try using the common fact that $\ln(x) \ll x^p$ for large $x$ but that of course only bounds it from below with a convergent series saying nothing about ours. Also I tried rewriting the 'summand' as $e^{\ln(k^{\ln k})}=e^{\ln k \cdot \ln k}$ but this did not really yield anything.   Any answer or hint would be greatly appreciated. Why don't gksu/gksudo or launching a graphical application with sudo work with Wayland? I installed Ubuntu 17.10. Now I am having trouble with gksu:  $ gksu -dg synaptic No ask_pass set, using default! xauth: /tmp/libgksu-HgUjgQ/.Xauthority STARTUP_ID: gksu/synaptic/8760-0-alex-XPS-15-9530_TIME4974977 cmd[0]: /usr/bin/sudo cmd[1]: -H cmd[2]: -S cmd[3]: -p cmd[4]: GNOME_SUDO_PASS cmd[5]: -u cmd[6]: root cmd[7]: -- cmd[8]: synaptic buffer: -GNOME_SUDO_PASS- brute force GNOME_SUDO_PASS ended... Yeah, we're in... Unable to init server: Could not connect: Connection refused (synaptic:8767): Gtk-WARNING **: cannot open display: :1 xauth: /tmp/libgksu-HgUjgQ/.Xauthority xauth_env: (null) dir: /tmp/libgksu-HgUjgQ   If I don't use -g, the password dialog is disabled. So looks like a problem with creating a tty for root.  Any advice? System.CalloutException: You have uncommitted work pending I have same exception can please   The previous post issue is resolved.  Exception: :System.CalloutException: You have uncommitted work pending. Please commit or rollback before calling out  Visualforce Page   &lt;apex:page controller="Controller" action="{!init}" showHeader="false" sidebar="false"&gt;     &lt;center&gt;         &lt;apex:pageBlock title="Request Listener"&gt;&lt;/apex:pageBlock&gt;               &lt;/center&gt; &lt;/apex:page&gt;   Controller :            PUBLIC with sharing class Controller {        PUBLIC String fromNumber      = ApexPages.currentPage().getParameters().get('From');     PUBLIC String toNumber        = ApexPages.currentPage().getParameters().get('To');     PUBLIC String body            = ApexPages.currentPage().getParameters().get('Body');        PUBLIC PageReference init()     {                    System.debug('From Phone Number :' +fromNumber);         System.debug('To phone NUmber :' + toNumber);         System.debug('Message Body :' + body);          TwilioRestClient Client = TwilioAPI.getDefaultClient();                                                                SYSTEM.DEBUG('FROM AND To  Number is NOT NULL');                      String formattedNumber='+919876543210';                 IF(body != NULL)                 body = body;             ELSE                 body = '';             Case c = NEW Case (Subject = formattedNumber,Description = body,Origin = 'Phone');             INSERT c;                               Map&lt;String,String&gt; params1 = new Map&lt;String,String&gt;             {                'To'   =&gt; fromNumber,                'From' =&gt; '+1908280****',                'Body' =&gt; 'Conformation to customer'             };             TwilioMessage message = client.getAccount().getMessages().create(params1); /* Valid conformation SMS sent to the Customer.*/                                            return null ;     } }   While loin as admin then click preview on visualforce page executed but case is not created.I have checked the the debug log it throw the exception. Doubling the tails in two-sample permutation test Suppose we have two samples and we wish to determine if they are drawn from the same distribution, the samples A,B being composed of some integers say.  If we test this using a two-sample permutation test, specifically by looking at permutations where the differences in the means of the samples are as extreme as the difference observed: is there any reason to think that we can calculate the two-tailed p-value by looking at one tail and doubling the probability?  This is what it appears to say in my lecture notes, but I don't understand why we could assume that the tails are symmetrical (or why it doesn't entail that assumption). Explanations were not forthcoming. How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? Let's say we have the statistics given below  gender mean sd n f 1.666667 0.5773503 3 m 4.500000 0.5773503 4   How do you perform a two-sample t-test (to see if there is a significant difference between the means of men and women in some variable) using statistics like this rather than actual data?  I couldn't find anywhere on the internet how to do this. Most of the tutorials and even the manual deal with the test with the actual data set only. $(a,b) \mathbin\# (c,d)=(a+c,b+d)$ and $(a,b) \mathbin\&(c,d)=(ac-bd(r^2+s^2), ad+bc+2rbd)$. Multiplicative inverse? Let $r\in \mathbb{R}$ and let $0\neq s \in \mathbb{R}$. Define operations $\#$ and $\&amp;$ on $\mathbb{R}$ x $\mathbb{R}$ by $(a,b) \mathbin\#(c,d)=(a+c,b+d)$ and $(a,b) \mathbin\&amp;(c,d)=(ac-bd(r^2+s^2), ad+bc+2rbd)$ as addition and multiplication, respectively. Do these operations form a field?  I have shown that every axiom of the field is satisfied except for the "existence of multiplicative inverses" axiom. This is where I need help. We either need to show that this axiom fails and so we don't have a field or that the axiom $aa^{-1}=1$ is satisfied for every $a\neq 0 \in \mathbb{R}$  The multiplicative identity in this problem is $(1,0)$.  Any solutions or hints are greatly appreciated. How does extra damage work for critical hits? I'm a bit confused on how extra damage works for critical hits. Let's take the following example: A thief with sneak attack rolls a crit. I'm under the impression he rolls double his normal attack damage dice AND double his Sneak Attack damage dice. Is this accurate? Another example, I finished DM-ing my first campaign recently. The Giant Spider enemy monster has an melee attack that causes a constitution saving throw. If the player fails, the enemy rolls an additional 2D8 of damage. In this situation, if there was a critical hit, and the player failed their saving throw, would I also roll double dice on the additional damage? Or is that considered a separate attack? Is there any method to close connection similar to  for  in WordPress?  Is it not necessary to close connection for global $wpdb? Can humans eat grass? Can a human eat grass and digest it? Could it be possible to use it as food just like other plants such as wheat or beans? Short description of the scoping rules? One-dimensional [Noetherian] UFD is a PID How can I verify the following statement?     The image of a morphism $f : A \longrightarrow B$ is defined as $\text{Im}(f) = \text{Ke}r(\text{coke}r f)$ whenever it exists (e.g., in every abelian category). The morphism $f : A \longrightarrow B$ factors   uniquely through $\text{Im} f \longrightarrow B$ whenever $\text{Im} f$ exists, and $A \longrightarrow \text{Im} f$ is an epimorphism and a cokernel of ker $f \longrightarrow A$ in every abelian category. How can I make a time delay in Python? I would like to know how to put a time delay in a Python script. Speed $v$ of a wave on a tightrope Is it safe to use a voltage divider for Arduino and DC motor controller?