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How do I remove an incomplete or broken snap installation of nextcloud on a Raspberry Pi? How to prove that derivatives have the Intermediate Value Property Suppose $X$ is a finite set and $f : X \to X$ is a function. Then $f$ is injective if and only if $f$ is surjective. Suppose $X$ is a set and $f : X \to X$ is a function.  If $X$ is a finite set, prove that $f$ is injective if and only if $f$ is surjective. Show that when $X$ is an infinite set, the statement is not true in general.   For that, let $X = \mathbb{R}$ and find a function $f: \mathbb{R} \to \mathbb{R}$ which is injective but not surjective, and a function $g: \mathbb{R} \to \mathbb{R}$ which is surjective but not injective  My attempt at the first part   Suppose that the function is surjective but not injective. Let $a,b \in X$ such that $f(a)=f(b)$ but $a \not =b$. Now since this is a finite set mapping to itself then there are not enough elements in $X$ to map to $X$ since two elements were used to map to one element, thus the function can't be surjective. Therefore if the function is surjective it is also injective.   Now suppose that the function is injective but not surjective. Let $a \in X$ such that $f(b)\not =a$ for all $b \in X$. Since the function was assusmed to be injective each $a \in X$ must map to an element of $X$, thus must have two elemetns in $X$ mapping to the same element in $X$. Hence the function can't be injective, therefore if the function is injective it must be surjective.   Would an exponetial function work for injective but not surjective since can't map to negative numbers. And an example of a function that is surjective but not injective could be a log function since none of the negative numbers get mapped to anything?   Also I'm having trouble seeing why it has to be finite for the first part to work. I understand it has something to do with the pigeonhole principle but its not that clear to me. What is this sand covered insect? I have found in a wooden house, in the mountains of central Spain this very curious insect:    I was wondering if that was its skin or whether it's decomposition or sand or saw-dust.  That particular region of Spain does have stink-bugs ... but this one doesn't look like anything I've seen before.  A google image search returns mostly arachnids ... but it seems to have only 6 legs. Let $P(x, y, 1)$ and $Q(x, y, z)$ lie on the curves $$\frac{x^2}{9}+\frac{y^2}{4}=4$$ and $$\frac{x+2}{1}=\frac{y-\sqrt{3}}{\sqrt{3}}=\frac{z-1}{2}$$ respectively. Then find the square of the minimum distance between $P$ and $Q$.  My Attempt is:  I tried to find minimum distance between the points $(-2,\sqrt{3})$ and $(6\cos \theta,4\sin \theta)$. "a ten years old boy" or "a ten year old boy" I was chatting with a friend after I saw his photos in Russia (Petersburg). He is a white British dude who has been to many, many, many countries. On the other hand, I am a pure Arab who looks like a typical Middle Easterner or North African, who has also been to many countries, but never to Russia or its neighbors.  Anyway, it seemed like he really liked Russia, so I told him it will be in my list. He told me "you do not belong".  At first, I wasn't sure what he did mean. He started explaining and told me stuff like "you will be hassled for no reason in some parts of the city" and "the police will stop you every few hundred meters asking for money". He made sure to make me believe that's all because I do not belong.  Can someone clarify this? Of course, some of this is hyperbole to help convey the point, but to what extent?  Note: The friend is . If you think the question is wrong, feel free to downvote him ;) "Communicate over" vs. "communicate through" Also schemas can communicate over database links to schemas in other remote databases.    Could one replace the preposition over with through? Will it change the meaning, and if so, when should we use over instead of through? Why don't Lightroom or PSE recognize CR2 files from my Canon 7D mk II even though they are up to date? Polite or unrectified placement of the word please how can I find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $? It is so weird for me because I put this to Mathematica and it tells me that sum does not converge...  Let consider sum no to infinity, but to n  $$ \sum_{k=1}^{n} (k\cdot \ln \frac{2k+1}{2k-1} - 1) =$$ $$ ln \frac{3}{1}\cdot \left(\frac{5}{3}\right)^2 \cdot...\cdot \left(\frac{2n+1}{2n-1}\right)^n - n = ln \frac{1}{1}\cdot \frac{1}{3}\cdot \frac{1}{5}\cdot ... \frac{1}{2n-1} - n $$ but $$ n = ln e^n $$ so it will be $$ln\frac{1}{e^n} \cdot \frac{1}{1}\cdot \frac{1}{3}\cdot \frac{1}{5}\cdot ... \frac{1}{2n-1}$$  So the limit of it is $-\infty$ Have I done this well or I missed sth? how to convert System::String to const char*? How do I send an HTTP request in C# without using System.Net classes? Switching to HTTPS - redirect question Importing coordinate data from Excel into QGIS I have an Excel file containing data collected over many years as latitude and longitude coordinates for archaeological sites. How can I import it into QGIS as a new layer? Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces Convert all text from uppercase to lowercase and vice versa? My question is how can I convert all text from uppercase to lowercase and vice versa? That is to change the cases of all the letters. It has to be done with a sed replacement somehow. How do you prove that these four definitions of the operator norm are equivalent? $$\begin{align*} \lVert A\rVert_{\mathrm{op}} &amp;= \inf\{ c\;\colon\; \lVert Av\rVert\leq c\lVert v\rVert \text{ for all }v\in V\}\\ &amp;=\sup\{ \lVert Av\rVert\;\colon\; v\in V\text{ with }\lVert v\rVert\leq 1\}\\ &amp;=\sup\{\lVert Av\rVert\;\colon\; v\in V\text{ with }\lVert v\rVert = 1 \}\\ &amp;=\sup\left\{ \frac{\lVert Av\rVert}{\lVert v\rVert}\;\colon\; v\in V\text{ with }v\neq 0\right\}. \end{align*}$$ What's the fastest way to make money online? Everything in the online world is expensive, well the best things are. We all want the luxurious apartment with 10 cars garage and the best weapons but to achieve that, we need money. Which missions or activities give the most cash ? Removing a DE field when DE is used in a data relationship I have a Data Extension field I'd like to delete, but that DE is used in an attribute group/set in Contact Builder. So is it really necessary to delete the data relationship first before I can remove the field? Seems too risky if that's the case.