I'm writing a report right now (in an article class, I know.. But I didn't want to have a Chapter as my top level of organization), and the report guidelines specify a memorandum/letter of submittal after the title page.   I was wondering if it's possible to have an "environment" of a memo (TexMemo is one I saw a lot while googling this question) inside my article class.     Thank you!
Let's say I have a document that has many pages and some pages have different formats. For example, most of the pages are fine with \documentclass{article} but there may be pages in the middle that I want to be \documentclass{letter}. I want my letter pages to be numbered inline with the other pages and have them show up in the Table of Contents.   Is it possible to change the class used for an individual or range of pages while still keeping things like page numbering consistent across them?   EDIT I'm trying to create a "welcome to the company" sort of document that has a cover page, table of contents, welcome letter, then various sections of information. I've never tried this in anything other than a word processor where it's easy to set "master pages" or "template pages" for individual pages in the document. So I could use a letterhead template page for the welcome letter part and a standard article-type template for the rest and still have the letter numbered/referenced in the ToC.   So the idea was to take advantage of the classes written, if possible, rather than have to format a single page by hand differently from the rest.
How to transfer a DVD to my hard drive Is there a C++ decompiler? Suppose $X$ is infinite and $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous Suppose that $X$ is infinite and that $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous.     My attempt:  Let $|A|=n$. We will prove by induction on n. It's clear that the the theorem is trivially true for $n=0$. Assume the theorem is true for all $n=k$. For $n=k+1$, then $|A \setminus \{a\}|=k$ for some $a \in A$. Thus $X \setminus (A \setminus \{a\}) \sim X$ by inductive hypothesis, or $(X \cap \{a\}) \cup (X \setminus A) \sim X$, or $\{a\} \cup (X \setminus A) \sim X$. We have $\{a\} \cup (X \setminus A) \sim X \setminus A$ since the theorem is true for $n=1$. Hence $X \setminus A \sim \{a\} \cup (X \setminus A) \sim X$. Thus $X \setminus A \sim X$. This completes the proof.       Does this proof look fine or contain gaps? Do you have suggestions? Many thanks for your dedicated help!     Update: Here I prove that the theorem is true for $n=1$.  Assume that $A = \{a\}$ and consequently $X \setminus A= X \setminus\{a\}$. It's clear that $|X \setminus A| \le |X|$. Next we prove that $|X| \le |X \setminus A|$. Since $X$ is infinite, there exists $B \subsetneq X$ such that $B \sim X$ (Here we assume Axiom of Countable Choice). Thus $|X|=|B|$. There are only two possible cases.   $a \in X \setminus B$   Then $B \subseteq X \setminus \{a\}=X \setminus A$ and consequently $|X|=|B| \le |X \setminus A|$. Thus $|X| \le |X \setminus A|$ and $|X \setminus A| \le |X|$. By Schröder–Bernstein theorem, we have $|X \setminus A| = |X|$. It follows that $X \setminus A \sim X$.   $a \in B$.   Let $b \in X \setminus B$. We define a bijection $f:X \setminus \{a\} \to X \setminus \{b\}$ by $f(x)= x$ for all $x \in X \setminus \{a,b\}$ and $f(b)=a$. Thus $X \setminus \{a\} \sim X \setminus \{b\}$. Since $b \in X \setminus B$, it follows from Case 1 that $X \setminus \{b\} \sim X$. Hence $X \setminus \{a\} \sim X \setminus \{b\} \sim X$. Thus $X \setminus \{a\} = X \setminus A \sim X$.  To sum up, $X \setminus A \sim X$ for all $|A|=1$. Remove subscribers from Auto Suppression List How to remove specific elements in a numpy array Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$ I'm working on this problem already, the domain and co-domain are the set of Rational Numbers. we see that setting $x = 1$ and $y = n$, we obtain $f(n + 1) = f(n) + 1$  But I'm trying to prove that $f(n) = n + 1$ for all $n$, the case when $n = 1, 2$ is obviously true, how do I approach this via induction? Cheese from UHT Milk I live in a town where fresh or whole milk is not readily available. I was wondering if I could make cheese from UHT Milk. If so, what kind of cheese and what method I should use? Or rather, Should I? If I have a $2\times 2$ or $3\times 3$ matrix, how should I go about computing the eigenvalues and eigenvectors of the matrix?  NB: I am making this question to provide a unified answer to questions about eigenvalues of small matrices so that all of the specific examples that come up can be marked as duplicates of this post. See . Manipulating Partial Derivatives of Inverse Function In lectures we're told:  $$\dfrac {\partial y} {\partial x} = \dfrac 1 {\dfrac {\partial x} {\partial y}}$$  as long as the same variables are being held constant in each partial derivative.  The course is 'applied maths', i.e non-rigorous, so don't confuse me.  But anyway, if we have:  $$\xi = x - y \qquad \eta = x$$  Then $\dfrac {\partial x} {\partial \xi} = 0$ and $\dfrac {\partial \xi} {\partial x} = 1$.  The rule presumably fails because one of the partial derivatives is $0$.  But then isn't this rule useless? Since I cannot use it without checking that the partial derivative isn't in fact $0$, but then I've worked out the partial derivative manually anyway. What are the differences between a multidimensional array and an array of arrays in C#? Do not enumerate a section, but add it into table of contents How do I rid of number of a section in the way that it still would be in the table of contents.  If I use   ... \section{SN1} ...   then I see this section name in table of contents as   1 SN1  2 SN2  3 SN3  ...   If I use   \section*{SN}   I don't see it in the content:   1 SN2  2 SN3   How to get in content just   SN1  1 SN2  2 SN3   ? I'm having a difficult time understanding this statement. Can someone please explain with a concrete example? Coloring specific elements of sets with a prime modified order in an array plot What's the best option to display Unicode text (hebrew, etc.) in VB6 I have some customers who want to use our speech therapy software in Hebrew.  The programs are in VB6. The best option I'm aware of are:   use the Forms 2.0 controls from MS Office, but you can't distribute them.    $899   $499   Any other options? Is time travel possible? Is it possible to go back in time? I read somewhere that according to relativity, it is possible - involving black holes and other stuff - to jump into the past. Is it possible for anything to go back in time either continuously or by jumping? Fastest Gun in the West Problem How do you choose Spells Known when creating a new character above 1st level? It's not clear to me how to choose Spells Known when creating a new character at a higher level.  Let's take the Bard as a working example first:  Bard level 2:   Spells Known: 5 Slots per Spell level: 1st &times; 3   Bard level 3:   Spells Known: 6 Slots per Spell level: 1st &times; 4, 2nd &times; 2   I'm interpreting this to mean that, if an existing 2nd-level Bard gains a new level (level 3), he's gaining 1 (one) new spell known. He can then choose the new spell known to be either 1st or 2nd, correct?  What I don't understand then, is the case of creating a new character starting at a higher level; say, creating a new Bard at level 3.  In that case you're forced to choose 6 spells, which must be from the list of 1st- and 2nd-level spells, correct?  When making this 3rd-level Bard from scratch, though, can I select 2nd level spells for all 6 spells known?  As another example, say you're creating a very high level Bard from scratch, starting at level 15. The book says your Spells Known is 19, and your spell slots are 1st × 4, 2nd × 3, 3rd × 3, 4th × 3, 5th × 2, 6th × 1, 7th × 1, and 8th × 1.  So, for those 19 Spells Known, you can choose any spells from 1st through 8th spell level. Am I free then to select as many spells as I can at 8th spell level (5 in number), working backwards, and in the end ignoring the 1st, 2nd, 3rd level spells entirely?  As another example, the Ranger doesn't know any spells at 1st level, nor have any spell slots, but the book says “You know two 1st-level spells of your choice from the ranger spell list.” Does it mean at 2nd level and above?  Long story short: When choosing Spells Known for a spellcasting character created above 1st level, am I allowed to choose my Spells Known at whatever spell level I like, just so long as I have at least one spell slot of that level?  I'm working on a D&amp;D 5e character generator and need to clarify this. property not working with getter AND setter How to pass Unicode characters as JSP/Servlet request.getParameter? If  $$\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$$ then prove that  $$\sin 2A \quad\text{ is a root of }\quad x^2 - 44x - 36 = 0$$  I have no idea how to solve it. Plz help.