The following is basic information about our forum. Please read this before posting questions or answers if you are unfamiliar with this sort of forum. Click on any question to show or hide the answer.
• What kinds of questions can I ask here?
• Most importantly, questions should be relevant to our community. Before you ask, please make sure to search for a similar question. You can search for questions by their title or tags.
• What kinds of questions should be avoided?
• Please avoid asking questions that are not related to our community, too subjective or argumentative.
• What should I avoid in my answers?
• Dettonville Answers is a question and answer site - it is not a discussion group. Please avoid holding debates in your answers as they tend to dilute the quality of the forum.

• How to enter mathematical notation?
• For Greek letters, use \alpha, \beta, …, \omega: $\alpha, \beta, … \omega$. For uppercase, use \Gamma, \Delta, …, \Omega: $\Gamma, \Delta, …, \Omega$.

• For superscripts and subscripts, use ^ and _. For example, x_i^2: $x_i^2$.

• By default, superscripts, subscripts, and other operations apply only to the next "group". A "group" is either a single symbol, or any formula surrounded by curly braces {}. If you do 10^10, you will get a surprise: $10^10$. But 10^{10} gives what you probably wanted: $10^{10}$. Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is ${x^y}^z$, and x^{y^z} is $x^{y^z}$. Observe the difference between x_i^2 $x_i^2$ and x_{i^2} $x_{i^2}$.

• Parentheses Ordinary symbols ()[] make parentheses and brackets $(2+3)[4+4]$. Use \{ and \} for curly braces $\{\}$.

These do not scale with the formula in between, so if you write (\frac12) the parentheses will be too small: $(\frac12)$. Using \left(\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac12\right) is $\left(\frac12\right)$.

\left and\right apply to all the following sorts of parentheses: ( and ) $(x)$, [ and ] $[x]$, \{ and \} $\lbrace x \rbrace$, | $|x|$, \langle and \rangle $\langle x \rangle$, \lceil and \rceil $\lceil x \rceil$, and \lfloor and \rfloor $\lfloor x \rfloor$. There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is $\left.\frac12\right\rbrace$.

• Sums and integrals \sum and \int; the subscript is the lower limit and the superscript is the upper limit, so for example \sum_1^n $\sum_1^n$. Don't forget {} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is $\sum_{i=0}^\infty i^2$. Similarly, \prod $\prod$, \int $\int$, \bigcup $\bigcup$, \bigcap $\bigcap$, \iint $\iint$.

• Fractions There are two ways to make these. \frac ab applies to the next two groups, and produces $\frac ab$; for more complicated numerators and denominators use {}: \frac{a+1}{b+1} is $\frac{a+1}{b+1}$. If the numerator and denominator are complicated, you may prefer \over, which splits up the group that it is in: {a+1\over b+1} is ${a+1\over b+1}$.

• For inline formulas, enclose the formula in $$...$$. For displayed formulas, use $$...$$.

These render differently as can be seen in the following two examples:

"$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$" appears as $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$ (inline)

whereas

"$$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\tag{displayed}$$" appears as $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}\tag{displayed}$$

• Fonts

• Use \mathbb or \Bbb for "blackboard bold": $\mathbb{CHNQRZ}$.
• Use \mathbf for boldface: $\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ $\mathbf{abcdefghijklmnopqrstuvwxyz}$.
• Use \mathtt for "typewriter" font: $\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ $\mathtt{abcdefghijklmnopqrstuvwxyz}$.
• Use \mathrm for roman font: $\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$ $\mathrm{abcdefghijklmnopqrstuvwxyz}$.
• Use \mathcal for "calligraphic" letters: $\mathcal{ ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
• Use \mathscr for script letters: $\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$
• Use \mathfrak for "Fraktur" (old German style) letters: $\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}$.
• Radical signs Use sqrt, which adjusts to the size of its argument: \sqrt{x^3} $\sqrt{x^3}$; \sqrt[3]{\frac xy} $\sqrt[3]{\frac xy}$. For complicated expressions, consider using {...}^{1/2} instead.

• Some special functions such as "lim", "sin", "max", "ln", and so on are normally set in roman font instead of italic font. Use \lim, \sin, etc. to make these: \sin x $\sin x$, not sin x $sin x$. Use subscripts to attach a notation to \lim: \lim_{x\to 0} $$\lim_{x\to 0}$$

• There are a very large number of special symbols and notations, too many to list here; see this shorter listing, or this exhaustive listing. Some of the most common include:

• \lt \gt \le \ge \neq $\lt\, \gt\, \le\, \ge\, \neq$. You can use \not to put a slash through almost anything: \not\lt $\not\lt$ but it often looks bad.
• \times \div \pm \mp $\times\, \div\, \pm\, \mp$. \cdot is a centered dot: $x\cdot y$
• \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing $\cup\, \cap\, \setminus\, \subset\, \subseteq \,\subsetneq \,\supset\, \in\, \notin\, \emptyset\, \varnothing$
• {n+1 \choose 2k} or \binom{n+1}{2k} ${n+1 \choose 2k}$
• \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto $\to\, \rightarrow\, \leftarrow\, \Rightarrow\, \Leftarrow\, \mapsto$
• \land \lor \lnot \forall \exists \top \bot \vdash \vDash $\land\, \lor\, \lnot\, \forall\, \exists\, \top\, \bot\, \vdash\, \vDash$
• \star \ast \oplus \circ \bullet $\star\, \ast\, \oplus\, \circ\, \bullet$
• \approx \sim \cong \equiv \prec $\approx\, \sim \, \cong\, \equiv\, \prec$.
• \infty \aleph_0 $\infty\, \aleph_0$ \nabla \partial $\nabla\, \partial$ \Im \Re $\Im\, \Re$
• For modular equivalence, use \pmod like this: a\equiv b\pmod n $a\equiv b\pmod n$.
• \ldots is the dots in $a_1, a_2, \ldots ,a_n$ \cdots is the dots in $a_1+a_2+\cdots+a_n$
• Some Greek letters have variant forms: \epsilon \varepsilon $\epsilon\, \varepsilon$, \phi \varphi $\phi\, \varphi$, and others. Script lowercase l is \ell $\ell$.
• Who moderates this community?
• The short answer is: you. This website is moderated by the users. Points system allows users to earn rights to perform a variety of moderation tasks.
• How does point system work?
• When a question or answer is voted up, the user who posted it will gain points. These points serve as a rough measure of the community trust in that person. Various moderation tasks are gradually assigned to the users based on those points.

For example, if you ask an interesting question or useful answer, it will likely be voted up. On the other hand if the question is poorly-worded or the answer is misleading - it will likely be voted down. Each up vote on a question will generate 1 points, whereas each vote against will subtract 1 points. The following table lists points gained per activity:

The following table lists point requirements for each type of moderation task.

 Voting posts down 100 points Voting on answers 100 points Voting on questions 100 points

The following table lists the user titles based on points:

• Wizard - 250,000 points

• Necromancer - 128,000 points

• Sorcerer - 64,000 points

• Warlock - 32,000 points

• Enchanter - 16,000 points

• Magician - 8,000 points

• Thaumaturgist - 4,000 points

• Theurgist - 2,000 points

• Conjurer - 1,000 points

• Evoker - 500 points

• Prestidigitator - 50 points

• How to change my picture (gravatar), and what is gravatar?
• The picture that appears in user profiles is called a gravatar, which means globally recognized avatar.

Please personalize your account with an image - just register at gravatar.com (just please be sure to use the same email address that you used to register with us). The default gray image is generated automatically.
• What is proper forum etiquette?
• The rules on etiquette on this site are very simple – be nice, be honest and speak to others as you expect others to speak to you.

Be warned – repeat offenders will be kicked off this site. Sure you can rejoin under a new email but you’ll lose all your hard earned rep and will end up booted off again if you break the rules.

Don’t flame on others if it seems they don’t know as much as you – be tolerant. Everyone on this site is here to learn and teach.