Name that nuclear holocaust survival book
Teenage girl in life-sustaining valley on poisoned Earth visited by another survivor
Group presentation for discrete Heisenberg group How to stop Tkinter Frame from shrinking to fit its contents? This is the code that's giving me trouble.   f = Frame(root, width=1000, bg="blue") f.pack(fill=X, expand=True)  l = Label(f, text="hi", width=10, bg="red", fg="white") l.pack()   If I comment out the lines with the Label, the Frame displays with the right width.  However, adding the Label seems to shrink the Frame down to the Label's size.  Is there a way to prevent that from happening? Get table names using SELECT statement in MySQL I found this odd relationship, $x^2 = \sum_\limits{k = 0}^{x-1} (2k + 1)$. Let $a, b, \&amp; \, m$ be integers. Prove that if $2a + 3b \geq 12m + 1$, then $a \geq 3m + 1$ or $b \geq 2m + 1$.   My Attempt: I don't conceive apace how to contrive, from the one inequality in the antecedent, the two inequalities in the consequent. So a proof by contraposition may be more facile. The contrapositive is: $\text{If }  \color{Green}{a &lt; 3m + 1} \; \&amp; \; \color{#0073CF}{b &lt; 2m + 1}, \text{ then } 2a + 3b &lt; 12m + 1 \tag{*}.$  From $(*)$, $\color{Green}{2a} + \color{#0073CF}{3b} &lt; \color{Green}{6m + 2} \; + \;\color{#0073CF}{6m + 3} = 12m +5$. But this doesn't prove $(*)$.     Given Solution:  Assume that $a &lt; 3m+1$ and $b &lt; 2m+1.$ Since a and b are integers, $a ≤ 3m$ and $b ≤ 2m.$ Therefore, $2a + 3b ≤ 2(3m) + 3(2m) = 12m &lt; 12m+ 1,$ as desired. $\blacksquare$   What went wrong in my attempt? I understand the given solution but I persisted with the more natural and direct green and blue, instead of deviating to weak inequalities. Shouldn't both solutions work?  Source: Problem 4.19 on P102 (related to P90, Result 4.8) of Mathematical Proofs, 2nd ed by Chartrand et al.    $\large{\text{Supplement to Cameron Buie and pritam's Answers :}}$  What overriding, catholic lessons can be extrapolated from this example to generalise about inequalities?   Moreover, in order to circumvent the problem here (ie the loss of information from the weaker inequalities), should I always start with the strictest inequality? If so, should I always rework any weak inequality into the equivalent strict inequality?   For example, define $r \in \mathbb{R} $ and $n \in \mathbb{Z}$ and $g(...) \neq h(...)$. Then $ f(r) &lt; h(r) \require{enclose}      \enclose{updiagonalstrike}{\iff} f(r) \leq g(r).$ But $ f(n) &lt; h(n) \text{ MAY OR MAY NOT }\iff f(n) \leq g(n).$ Shouldn't it be "he was the most famous fighter to have ever lived"? How to prevent different checksums for different typesets 1 Plot, 2 Scale/Axis Let $X \subset L^1(\mathbb{R})$ a closed linear subspace satisfying \begin{align} X\subset \bigcup_{p&gt;1} L^p(\mathbb{R})\end{align}    Show that $X\subset L^{p_0}(\mathbb{R})$ for some $p_0&gt;1.$   I guess the problem is that in infinite measure spaces the inclusion $L^p\subset L^q$ only holds for $p=q$. Is it maybe possbile to apply Baire's Theorem in some way? Most of the time, I use good and well interchangeably. However, on many occasions I would find well or good a misfit. Please suggest the proper usage. I'm new here. Can anyone give me a hint in this problem? Please.  Let $X$ be a topological space. If $f,g$ are continuous function of $f,g\colon X\to S^n$  which $f(x)\neq -g(x)$ for all $x$ in $X$, show $f$ and $g$ are homotopics. I try to show a homotopy using $$q(x) = \frac{f(x)+g(x)}{\|f(x)+g(x)\|}$$ it's well defined, but i'm stuck. What does the (unary) * operator do in this Ruby code? Config files for assemblies in GAC Show/Hide function folding margin on Notepad++ Is it possible to get rid of the function folding margin on Notepad++? It seems like the sort of thing that should be in the prefs but I'm not seeing it anywhere. I've browsed the forums and found a number of posts that have addressed this issue, but none of the solutions seem to work for me. I have the following script that I just copied from the bibtex home page to get familiar with it. Instead of the citation number I get a question mark. I compile using Latex+Bibtex+Latex+Latex+PDFLatex+ViewPDF just as has been previously suggested and the problem persists.   \documentclass[11pt]{article} \usepackage{cite}  \begin{document}  \title{My Article} \author{Nobody Jr.} \date{Today} \maketitle  Blablabla said Nobody ~\cite{Nobody06}.  \bibliography{mybib} \bibliographystyle{plain} \end{document}   My bibliography (Bib.bbl)  @misc{ Nobody06, author = "Nobody Jr", title = "My Article", year = "2006" }    Looking at previous posts one thing that is concerning is that my .bbl looks empty as shown below. Further, I don't have a .blg  \begin{thebibliography}{}  \end{thebibliography} How can I utilize the whole terminal, like htop or emacs do? I want to write a program that can "draw" in the terminal the same way as htop or emacs. By that I mean "get rid of the prompt and make the output dependent on the current size of the terminal".   To make this a bit more clear:   I want to use the terminal this way:     in stead of this way: Pick a class that has access to the Extra Attack feature. For my example, I'll use my standby, Fighter McFighterson.  Let us say that McFighterson is 20th level, and possesses the Dual Wielder feat. He is currently holding a greatsword, and has two longswords accessible.  As a reminder, two weapon fighting says:     When you take the Attack action and attack with a light melee weapon that you're holding in one hand, you can use a bonus action to attack with a different light melee weapon that you're holding in the other hand...[snip]   And Dual Wielder:     [snip]... You can use two-weapon fighting even when the one handed melee weapons you are wielding aren’t light.   You can draw or stow two one-handed weapons when you would normally be able to draw or stow only one. ...[snip]   Can McFighterson make all of the attacks granted by Extra Attack (3, in this case) with his greatsword, drop the greatsword "for free", draw two longswords (as permitted by Dual Wielder), use his last attack to attack with one longsword, then two-weapon-fight with the second longsword?  Making the attack sequence look something like: Greatsword, Greatsword, Greatsword, Longsword1, Longsword2.    Related: Can I travel to Dublin, Republic of Ireland with UK Tier 2/Schengen visas with Indian Passport How do I clone a generic list in C#? Why is $\arctan(x)=x-x^3/3+x^5/5-x^7/7+\dots$?  Can someone point me to a proof, or explain if it's a simple answer?  What I'm looking for is the point where it becomes understood that trigonometric functions and pi can be expressed as series.  A lot of the information I find when looking for that seems to point back to arctan.