Hashmap throwing nullpointer exception when trying to get Integer value
What is a NullPointerException, and how do I fix it?
If $x,y,z\in\mathbb R\setminus \{1\}$ and $xyz=1$, prove that $\frac{x^2}{(x-1)^2}+\frac{y^2}{(y-1)^2}+\frac{z^2}{(z-1)^2}\ge 1$. I can't get into my field research prize I would like to install Ubuntu  for almost 120 users. But it's very difficult in using USB and drives.  Any suggestions? When installing user applications, where do "best practices" suggest they be located? Occasionally I install applications manually, rather than using apt or another package manager.   What location (/usr/, /usr/local/, /opt/, /home/, etc.) is suggested by "best practices" for the installation of user applications? 15V 3A dc motor PWM frequency setting What is a suitable frequency for 15V/3A DC motor? Is there any effect on the motor when the frequency is changing? I am confused with this until now and the Internet shows a lot of theory that confuses me. Customize newform save button - Save and redirect to another form What is the best way to add redirect function into the save button on a newform in SharePoint 2013.  When the user create a list item, he/she should be redirected to another form. Is it possible to get and parse the new generated item ID?  Start - Newform URL:   End - Editform URL:   Thanks Replacing whiteness with transparency in Photoshop I want to replace the whiteness in pixels with transparency in the same way as described in  - i.e. for lighter pixels to be made proportionally as transparent. All solutions found via google are based on magic wand or other methods that do not work for my needs.  I'm sure there used to be a way to do this in earlier version of Photoshop (a simple functions to replace a colour with transparency), but I can't seem to do it in CS6.  Replace Colour has no alpha options.. I am Haitian, and traveling with a Haitian passport. I have to go to London with a work permit (tier 2 visa) on the 29th of July but I have 2 hour transit in Dublin.  Do I need a transit visa? Can I get it at the airport?  I also have a valid US visa. Finding an uncountable chain of subsets the integers How to find an uncountable subset of $P(\mathbb{N})$ such that every two elements of it can be compared. In fact, give an uncountable subset of $P(\mathbb{N})$ such that has totality property. We mean by $P(\mathbb{N})$, the powerset of natural numbers set $\mathbb{N}$. The following question is taken from Royden's Real Analysis $4$th edition, Chapter $3,$ question $28,$ page $67:$     Question: Show that Egoroff's Theorem continues to hold if the convergence is pointwise a.e. and $f$ is finite a.e., that is.       Assume $E$ has finite measure. Let $\{f_n\}$ be a sequence of measurable functions on $E$ that converges pointwise almost everywhere on $E$ to the real-valued function $f$ which is finite almost everywhere. Then for each $\varepsilon&gt;0,$ there is a closed set $F$ contained in $E$ for which    $$\{f_n\}\to f \text{ uniformly on }F \text{ and }m(E\setminus F)&lt;\varepsilon.$$   My attempt:   Let $A = \{ x\in E: f_n\not\to f \text{ pointwise} \}$ and $B=\{ x\in E: |f|=\infty \}.$  By assumption,  $$m(A)=m(B)=0.$$ So $A$ and $B$ are measurable.  Note that  $$m[E\setminus (A\cup B)] = m(E) - m(A\cup B) = m(E).$$ Fix $\varepsilon&gt;0.$ Since $\{f_n\}$ converges to $f$ pointwise on $E\setminus (A\cup B)$ to the real-valued function $f,$ by Egoroff's Theorem, there exists a closed set $F$ contained in $(E\setminus (A\cup B))\subseteq E$ for which  $$f_n\to f \text{ uniformly on } F \text{ and }m[(E\setminus(A\cup B)) \setminus F] &lt; \varepsilon.$$ Since $E$ has finite measure and $F\subseteq E,$ by monotonicity,  $F$ has finite measure. As $F$ is closed, it is also measurable.  Therefore, by Excision property, we have $$m(E\setminus F) = m(E) - m(F) = m[E\setminus(A\cup B)] - m(F) = m[(E\setminus(A\cup B)) \setminus F]&lt;\varepsilon.$$  Is my proof correct? I ask for verification because in this  Kenny's comment about countable union of null sets. I do not use this anywhere in my proof. So I wonder whether my proof miss out something. Why is it not possible to overload class templates? How can brackets be escaped in using string.Format? For example: String val = &quot;1,2,3&quot; String.Format(&quot; foo {{0}}&quot;, val);  This example doesn't throw an exception, but it outputs the string foo {0}. Is there a way to escape the brackets? Calculating frames per second in a game Maximum area of isosceles triangle with perimeter 6 cm Capital letters in "Theorem", "Conjecture" etc This is my first post and as you can probably guess I am a mathematician so I have no clue about grammar. I am writing a mathematical document at the moment and I would appreciate some advice on my usage of capital letters. Can somebody please confirm if the following are correct?  1) "We know by T​heorem 4.6.1 that..."   2) "the following c​onjecture, due to..."  3) In order to prove the "Mckay-Stevens $k$-covering C​onjecture, once needs to show that..."  I'm particularly confused about 3).  Many thanks for any help Prove that $a^{2^n}=1 \mod 2^{n+2}$ I would like to prove that  $$a^{2^n}\equiv 1 \pmod {2^{n+2}}$$  I tried induction but could not get it.  Thank you very much! network manager says "device not managed" Leaflet Customer Marker Changes Position with Scale How do I interpret the Mann-Whitney U when using R's formula interface "This site is all about getting answers. It's not a discussion forum. There's no chit-chat."