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# Help:MathJax Notation

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• To see how any formula was written in any question or answer, including this one, right-click on the expression and choose "Show Math As > TeX Commands". (When you do this, the '$' will not display. Make sure you add these. See the next point. There are also other possibilities how to view the code for the formula or the whole post.) For inline formulas, enclose the formula in$...$. For displayed formulas, use $$...$$. These render differently. For example, type$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$to show $$∑ni=0i2=(n2+n)(2n+1)6$$(which is inline mode) or type $$\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}$$ to show  i=0ni2=(n2+n)(2n+1)6 •  (which is display mode). • For Greek letters, use \alpha, \beta, …, \omega: $$α,β,…ω$$. For uppercase, use \Gamma, \Delta, …, \Omega: $$Γ,Δ,…,Ω$$. Some Greek letters have variant forms: \epsilon \varepsilon $$ϵ$$, $$ε$$, \phi \varphi $$ϕ$$, $$φ$$, and others. • For superscripts and subscripts, use ^ and _. For example, x_i^2: $$x2i$$, \log_2 x: $$log2x$$. • Groups. 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: $$1010$$. But 10^{10} gives what you probably wanted: $$1010$$. Use curly braces to delimit a formula to which a superscript or subscript applies: x^5^6 is an error; {x^y}^z is $$xyz$$, and x^{y^z} is $$xyz$$. Observe the difference between x_i^2 $$x2i$$ and x_{i^2} $$xi2$$. • 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 (\frac{\sqrt x}{y^3}) the parentheses will be too small: $$(x√y3)$$ . Using \left(\right) will make the sizes adjust automatically to the formula they enclose: \left(\frac{\sqrt x}{y^3}\right) is $$(x√y3)$$. \left and\right apply to all the following sorts of parentheses: ( and ) $$(x)$$ , [ and ] $$[x]$$, \{ and \} $${x}$$, | $$|x|$$, \vert $$|x|$$, \Vert $$∥x∥$$, \langle and \rangle $$⟨x⟩$$, \lceil and \rceil $$⌈x⌉$$, and \lfloor and \rfloor $$⌊x⌋$$. \middle can be used to add additional dividers. There are also invisible parentheses, denoted by .: \left.\frac12\right\rbrace is $$12}$$. If manual size adjustments are required: \Biggl(\biggl(\Bigl(\bigl((x)\bigr)\Bigr)\biggr)\Biggr) gives $$(((((x)))))$$. • 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 $$∑n1$$. Don't forget {} if the limits are more than a single symbol. For example, \sum_{i=0}^\infty i^2 is $$∑∞i=0i2$$. Similarly, \prod $$∏$$, \int $$∫$$, \bigcup $$⋃$$, \bigcap $$⋂$$, \iint $$∬$$, \iiint $$∭$$, \idotsint $$∫⋯∫$$. • Fractions There are three ways to make these . \frac ab applies to the next two groups, and produces $$ab$$; for more complicated numerators and denominators use {}: \frac{a+1}{b+1} is $$a+1b+1$$. 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 $$a+1b+1$$. Using \cfrac{a}{b} command is useful for continued fractions $$ab$$, more details for which are given in this sub-article . 1. Fonts • Use \mathbb or \Bbb for "blackboard bold": $$CHNQRZ$$. • Use \mathbf for boldface: $$ABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxyz$$. • For expression based characters, use \boldsymbol instead: $$α$$ • Use \mathit for italics: $$ABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxyz$$. • Use \pmb for boldfaced italics: $$ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz$$. • Use \mathtt for "typewriter" font: $$ABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxyz$$. • Use \mathrm for roman font: $$ABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxyz$$. • Use \mathsf for sans-serif font: $$ABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxy$$. • Use \mathcal for "calligraphic" letters: $$ABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxyz$$ • Use \mathscr for script letters: $$ABCDEFGHIJKLMNOPQRSTUVWXYZ$$  $$abcdefghijklmnopqrstuvwxyz$$ • Use \mathfrak for "Fraktur" (old German style) letters: $$ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz$$ • . 1. Radical signs / roots Use sqrt, which adjusts to the size of its argument: \sqrt{x^3} $$x3−−√$$; \sqrt[3]{\frac xy} $$xy−−√3$$. 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 $$sinx$$, not sin x $$sinx$$. Use subscripts to attach a notation to \lim: \lim_{x\to 0}  limx0  Nonstandard function names can be set with \operatorname{foo}(x) $$foo(x)$$. 1. 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 \leq \leqq \leqslant \ge \geq \geqq \geqslant \neq $$<$$, $$>$$, $$≤$$, $$≤$$, $$≦$$, $$⩽$$, $$≥$$, $$≥$$, $$≧$$, $$⩾$$, $$≠$$. You can use \not to put a slash through almost anything: \not\lt $$≮$$ •  but it often looks bad. • \times \div \pm \mp $$×$$, $$÷$$, $$±$$, $$∓$$. \cdot is a centered dot: $$x⋅y$$ • \cup \cap \setminus \subset \subseteq \subsetneq \supset \in \notin \emptyset \varnothing $$∪$$, $$∩$$, $$∖$$, $$⊂$$, $$⊆$$, $$⊊$$, $$⊃$$, $$∈$$, $$∉$$, $$∅$$, $$∅$$ • {n+1 \choose 2k} or \binom{n+1}{2k} $$(n+12k)$$ • \to \rightarrow \leftarrow \Rightarrow \Leftarrow \mapsto $$→$$, $$→$$, $$←$$, $$⇒$$, $$⇐$$, $$↦$$ • \land \lor \lnot \forall \exists \top \bot \vdash \vDash $$∧$$, $$∨$$, $$¬$$, $$∀$$, $$∃$$, $$⊤$$, $$⊥$$, $$⊢$$, $$⊨$$ • \star \ast \oplus \circ \bullet $$⋆$$, $$∗$$, $$⊕$$, $$∘$$, $$∙$$ • \approx \sim \simeq \cong \equiv \prec \lhd \therefore $$≈$$, $$∼$$, $$≃$$, $$≅$$, $$≡$$, $$≺$$, $$⊲$$, $$∴$$ • \infty \aleph_0 $$∞ℵ0$$  \nabla \partial $$∇$$, $$∂$$ \Im \Re $$I$$, $$R$$ • For modular equivalence, use \pmod like this: a\equiv b\pmod n $$a≡b(modn)$$. • For the binary mod operator, use \bmod like this: a\bmod 17 $$amod17$$. Avoid using \mod, as it produces extra space: compare the above with a\mod 17 $$amod17$$. • \ldots is the dots in $$a1,a2,…,an$$\cdots is the dots in $$a1+a2+⋯+an$$Script lowercase l is \ell $$ℓ$$ • . Detexify lets you draw a symbol on a web page and then lists the $$TEX$$  symbols that seem to resemble it. These are not guaranteed to work in MathJax but are a good place to start. To check that a command is supported, note that MathJax.org maintains alist of currently supported LATEXcommands , and one can also check Dr. Carol JVF Burns's page ofTEXCommands Available in MathJax . 1. Spaces MathJax usually decides for itself how to space formulas, using a complex set of rules. Putting extra literal spaces into formulas will not change the amount of space MathJax puts in: a␣b and a␣␣␣␣b are both $$ab$$. To add more space, use \, for a thin space $$ab$$; \; for a wider space $$ab$$. \quad and \qquad are large spaces: $$ab$$, $$ab$$. To set plain text, use \text{…}: $${x∈s∣x is extra large}$$. You can nest$…$inside of \text{…}, for example to access spaces. 1. Accents and diacritical marks Use \hat for a single symbol $$x^$$, \widehat for a larger formula $$xyˆ$$. If you make it too wide, it will look silly. Similarly, there are \bar $$x¯$$ and \overline $$xyz¯¯¯¯¯¯¯¯$$, and \vec $$x⃗$$ and \overrightarrow $$xy−→$$ and \overleftrightarrow $$xy←→$$. For dots, as in $$ddxxx˙=x˙2+xx¨$$, use \dot and \ddot. Special characters used for MathJax interpreting can be escaped using the \ character: \\\$ , \{ $${$$, \_ $$_$$, etc. If you want \ itself, you should use \backslash (symbol) or \setminus ( binary operation
) for $$∖$$, because \\ is for a new line.