Balancing Attack to Defense in a text based RPG
How to develop RPG Damage Formulas?
I wanted a simple environment for making lists of equations, so I made one that includes an equation and a split environment. The code won't compile and the error seems unrelated. The most pressing thing I noticed was the &quot;You can't use `\end' in internal vertical mode.&quot; The problem is definitely the split environment. Here is a MWE. \documentclass{article} \usepackage{amsmath}  \newenvironment{env}     {\begin{equation}\begin{split}}     {\end{split}\end{equation}}  \begin{document} \begin{env}     x \end{env} \end{document}  If I remove the split environment from env, everything compiles just fine. Additionally, If the following example compiles just fine. What is the problem then? \documentclass{article} \usepackage{amsmath}  \begin{document} \begin{equation} \begin{split}     x \end{split} \end{equation} \end{document}  Here is the LaTeX error upon running the MWE. math.tex|11 error| LaTeX Error: \begin{split} on input line 9 ended by \end{env}. math.tex|12 error| LaTeX Error: \begin{equation} on input line 9 ended by \end{document}. math.tex|12 error| Missing $ inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing \cr inserted. math.tex|12 error| Missing { inserted. math.tex|12 error| Missing { inserted. math.tex|12 error| Extra }, or forgotten $. math.tex|12 error| Missing $ inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| You can't use `\end' in internal vertical mode. math.tex|12 error| LaTeX Error: \begin{equation} on input line 9 ended by \end{document}. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing $ inserted. math.tex|12 error| Display math should end with $$. math.tex|| Emergency stop. math.tex|| ==&gt; Fatal error occurred, no output PDF file produced! A continuous bijection from a compact space to a $T_2$ space is always a homeomorphism This problem is bugging me for some time.     $f:(X,\mathcal{T}) \to (Y,\mathcal{T}')$ is a continuous bijection where $(X,\mathcal{T})$ is compact and $(Y,\mathcal{T}')$ is $T_2$ (i.e. Hausdorff and $T_1$). Then show that $f$ must be a homeomorphism.   So far I have failed to understand any relation between the compactness of domain and $T_2$-ness of the range. I tried in vain to prove that $f(U)$ is open in $(Y,\mathcal{T}')$ whenever $U$ is so in $(X,\mathcal{T})$. I know $f$ makes $X$ and $Y$ respectively $T_2$ and compact and hence makes both of them $T_4$ spaces. But that is not coming to any use. I would be glad if someone helps me with a solution. Thank you. How can one prove that $\pi^4 + \pi^5 < e^6$? How does the unit circle work for trigonometric ratios of obtuse angles? I know that the x coordinate is $cos (\theta )$ and the y coordinate is $sin (\theta )$. But I understand these in context of only acute angles? I don't understand why the unit circle definition works for other than acute angles? Somebody please provide me some good intuition. Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square Finding the limit $\lim \limits_{n \to \infty}\ (\cos \frac x 2 \cdot\cos \frac x 4\cdot \cos \frac x 8\cdots \cos \frac x {2^n}) $ I've read a new study which suggests that yawning may help you keep a cool head. Also, the findings might hold some hope for sufferers of insomnia, migraines, and even epilepsy.  Is there any conclusion about what the function of yawning is and why do we yawn? How to find the determinant of this $3 \times 3$ Hankel matrix? Today, at my linear algebra exam, there was this question that I couldn't solve.   Prove that $$\det \begin{bmatrix}  n^{2} &amp; (n+1)^{2} &amp;(n+2)^{2} \\  (n+1)^{2} &amp;(n+2)^{2}  &amp; (n+3)^{2}\\  (n+2)^{2} &amp; (n+3)^{2} &amp; (n+4)^{2} \end{bmatrix} = -8$$   Clearly, calculating the determinant, with the matrix as it is, wasn't the right way. The calculations went on and on. But I couldn't think of any other way to solve it. Is there any way to simplify $A$, so as to calculate the determinant? Why don't I hear any sound after calling the Beep function in Windows 7? Metapost label based on variable value I want to label a scale based on a variable value and I wrote a metapost code like this.  $ := 1; for i = -.3cm step .6cm until 3.6cm:     label.bot(str$,(i,-3.7cm));     $ := incr($); endfor;   It just labels "$" instead of its value. How to output the variables value? Symbolizing layer with graduated colors by date/time field? I've got a layer of polygons where each has a date associated with it.  I want to color the polygons with graduated colors, but I want the colors to start with the newest polygons and fade to the oldest polygons.  So far I haven't been able to find a way to do this in ArcMap (&lt;= 9.3.1) other than to create a new field and calculate some integer or float value based on the date.  Is it possible to use a date or time field directly?   The data is natively a date-time value There are far too many records to use any unique-value renderer Converting the date to a numerical field is an answer for a different question. Meaning of "over in" I read this sentence in a book:     I just took part in a study over in the Psychology Department.   Why do we add over in front of in the here? Applying Dupli-Objects Is it possible to bake dupliverts into one mesh for the BGE? (I have a large ground landscape that I use as the parent to duplicate trees, and the BGE doesn't support most modifiers.) du shows completely different folder size for * and folder name I'm trying to move some data over and to start with I'd like to make sure that the size is ok. I run into a problem however, if I check the folder with   du -sh  myfolder/ 780M    myfolder/   but   du -sh * .. 71M     myfolder ..   I thought it might be something to do with hidden files but this particular folder does not have any inside.  Am I missing something? Should I use 'or' or 'nor' after a negative statement? This document does not cover the SDK interfaces nor any other reference material.   I think the above is correct, but my grammatical checker in Microsoft Word underlines nor and suggests or. Why? How did Harry remove the Philosopher's Stone from the Mirror of Erised? ‘How did I get the Stone out of the Mirror?’   ‘Ah, now, I’m glad you asked me that. It was one of my more brilliant ideas, and between you and me, that’s saying something. You see, only one who wanted to find the Stone – find it, but not use it – would be able to get it, otherwise they’d just see themselves making gold or drinking Elixir of Life.’   Philosopher's Stone - page 217 - Bloomsbury - chapter seventeen, The Man With Two Faces - Harry talking with Dumbledore   Dumbledore doesn't directly answer Harry's question, but rather describes under what circumstances a person could collect the Philosopher's Stone from the mirror. Did Harry have to do anything to retrieve the stone, such as reach into the mirror and take it? If not, what kind of magic could have removed the stone from the mirror and put it into Harry's possession?  A canon-based answer is preferred, such as the books, interviews with J.K. Rowling, or info from Pottermore, but subjective answers within the spirit of canon are welcome. What is this agglomeration of pink cells I found attached to a stone? Why isn't Google Chrome available in the Software Centre? Contraction of quotient ideal is quotient of contractions? How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$ is injective, then $\phi$ is also injective? How to show that when the linear transformation $\Phi =\psi \circ \phi : E \rightarrow G$  (where $\phi : E \rightarrow F$ and $\psi : F \rightarrow G$) is (1) injective, then $\phi$ is injective and when (2) $\Phi$ is surjective, then $\psi$ is also surjective ?  I've tried to prove it by the definition of injection and surjection, but I'm not convinced myself by it.  For example, in the first case :  If $\Phi$ is injective, $\forall g \in G$, we have $0$ or $1$ $e \in E$ such as $\Phi(e)=g$.  $\Rightarrow \Phi(e) = \psi(\phi(e)) = \psi(f) =g$.   So $\forall f \in F$, we also have $0$ or $1$ $e \in E$ such as $\phi(e)=f \in F$.   $\Rightarrow \phi$ is injective.  Is this right or did I prove nothing at all ? I think it is easier to convince myself/ to understand with surjectivity but still..