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 Alternatives: (mml file)  (full) (simple) (plain) (form) (slideshow) File: TortureTests/Complexity/complex4 CVS-ID: Author: Design Science, Inc. (D. Doyle, R. Miner) Description: Testing content tags. Sample Rendering: N/A

a + b - c

$a+b-c$

x + yz + z

$x+yz+z$

x * (y + z) * z

$x(y+z)z$

sin(a + b)

$\sin (a+b)$

sin(x(y + z)z)

$\sin (x(y+z)z)$

sin(xy)2b

$\sin (xy)2b$

(x + y) ^ (n - 3)

$(x+y)^{(n-3)}$

limit as x goes to a of sin x using <reln>

$\lim_{(x, a)}\sin x$

limit as x goes to a of sin x using <apply>

$\lim_{x\to a}\sin x$

limit as x goes to a of sin(x + y) using <reln>

$\lim_{(x, a)}\sin (x+y)$

limit as x goes to a of sin(x + y) using <apply>

$\lim_{x\to a}\sin (x+y)$

limit as x goes to a of sin(x + y)2b using <reln>

$\lim_{(x, a)}\sin (xy)2b$

limit as x goes to a of sin(x + y)2b using <apply>

$\lim_{x\to a}\sin (xy)2b$

quotient

$\left\lfloor\frac{a}{b}\right\rfloor$

moment

$\langle X^{3}\rangle$

selector

$\begin{pmatrix}1 & 2\\ 3 & 4\end{pmatrix}_{1}$

factorial

$n!$

(a + b)!

$(n+m+x)!$

inverse function

$f^{(-1)}$

inverse matrix

$a^{(-1)}(A)$

conjugate

$\overline{x+iy}$

a + b + c

$a+b+c$

integral (a + x)dx

$\int_{0}^{a} a+x\,d x$

-1 + 7

$-1+7$

7 + (-1)

$7+-1$

max

$\max\{x-\sin x, (x, 0)\land (x, 1)\}$

lambda sin(x + 1)

$\mathrm{lambda}\: x.\: \sin (x+1)$

lambda integral f(x)dx

$\mathrm{lambda}\: b.\: \int_{a}^{b} f(x)\,d x$

compose f and g

$f\circ g$

compose f and g (x)

$(f\circ g)(x)$

f(g(x))

$f(g(x))$

composition of f and inverse of f eq identity using <reln>

$(f\circ f^{(-1)}, \mathrm{id})$

composition of f and inverse of f eq identity using <apply>

$f\circ f^{(-1)}=\mathrm{id}$

e^x

$e^{x}$

min(x, x not in B, x^2) using <reln>

$\min\{x^{2}, (x, B)\}$

min(x, x not in B, x^2) using <apply>

$\min\{x^{2}, x\notin B\}$

a mod (b)

$a\mod b$

ab

$ab$

gcd(a b, c)

$\gcd (a, b, c)$

integral

$\int_{0}^{a} f(x)\,d x$

abs(x)

$\left|x\right|$

tall abs(x)

$\left|\frac{H}{K}\right|$

abs(x + y + z)

$\left|x+y+z\right|$

x > 0 and z < 1 as <reln>

$(x, 0)\land (x, 1)$

x > 0 and z < 1 as <apply>

$(x> 0)\land (x< 1)$

a and b

$a\land b$

a or b

$a\lor b$

a xor b

$a\mathop{\mathrm{xor}}b$

a eq b with <reln> tag

$(a, b)$

a eq b with <apply> tag

$a=b$

a neq b with <reln> tag

$(a, b)$

a neq b with <apply> tag

$a\neq b$

a > b with <reln> tag

$(a, b)$

a > b with <apply> tag

$a> b$

a < b with <reln> tag

$(a, b)$

a < b with <apply> tag

$a< b$

a <= b with <reln> tag

$(a, b)$

a >= b with <apply> tag

$a\ge b$

a <= b with <reln> tag

$(a, b)$

a <= b with <apply> tag

$a\le b$

set: {b, a, c}

$\{b, a, c\}$

set with condition

$\{x\colon (x, 5)\}$

list: {b, a, c}

$\left[b, a, c\right]$

list: {x|x < 5}

$\left[x\colon (x, 5)\right]$

A union B

$A\cup B$

A intersect B

$A\cap B$

A intersect (B union C)

$A\cap (B\cup C)$

integral x in R as <reln>

$(x, R)$

x in R as <apply>

$x\in R$

a in A

$(a, A)$

a not in A as <reln>

$(a, A)$

a not in A as <apply>

$a\notin A$

not a

$\neg a$

not (a and b)

$\neg (a\land b)$

A -> B (reln)

$(A, B)$

A -> B (apply)

$A\implies B$

forall

$\forall x\colon (x-x, 0)$

forall/and/lt/power

$\forall p, q, (p, Q)\land (q, Q)\land (p, q)\colon (p, q^{2})$

forall/exists/and/plus

$\forall n, (n, Z)\land (n, 0)\colon \exists x, y, z, (x, Z)\land (y, Z)\land (z, Z)\colon (x^{n}+y^{n}, z^{n})$

exists

$\exists x\colon (f(x), 0)$

forall/exists/and/plus

$\forall n, (n, Z)\land (n, 0)\colon \exists x, y, z, (x, Z)\land (y, Z)\land (z, Z)\colon (x^{n}+y^{n}, z^{n})$

ln a

$\ln a$

log base 3 of x

$\log_{3}x$

integer

$\int_{(x, D)} f(x)\,d x$

diff

$\frac{d f(x)}{d x}}$

partialdiff

$\frac{\partial^{3}f(x, y)}{\partial x^{2}\partial y}$

integral

$\int_{a}^{b} f(x)\,d x$

partialdiff

$\frac{\partial^{n+m}\sin (xy)}{\partial x^{n}\partial y^{m}}$

divide

$\frac{a}{b}$

divide/plus/minus

$\frac{a+b}{a-b}$

divide/plus/divide

$\frac{a+b}{\frac{a}{b}}$

A is subset of B as <reln>

$(A, B)$

A is subset of B as <apply>

$A\subseteq B$

A is proper subset of B as <reln>

$(A, B)$

A is proper subset of B as <apply>

$A\subset B$

A is not subset of B as <reln>

$(A, B)$

A is not subset of B as <apply>

$A\nsubseteq B$

A is not proper subset of B as <reln>

$(A, B)$

A is not proper subset of B as <apply>

$A\not\subset B$

Set difference

$A\setminus B$

Log base 3 of x + y

$\log_{3}(x+y)$

Sum as x goes from a to b of f(x)

$\sum_{x=a}^{b} f(x)$

sum

$\sum_{(x, B)} f(x)$

product

$\prod_{x=a}^{b} f(x)$

product

$\prod_{(x, B)} f(x)$

tendsto with <reln>

$(x^{2}, a^{2})$

tendsto with <apply>

$x^{2}\to a^{2}$

tendsto with <reln>

$(\left(\begin{array}{c}x\\ y\end{array}\right), \left(\begin{array}{c}f(x, y)\\ g(x, y)\end{array}\right))$

tendsto with <apply>

$\left(\begin{array}{c}x\\ y\end{array}\right)\to \left(\begin{array}{c}f(x, y)\\ g(x, y)\end{array}\right)$

mean(X)

$\langle X\rangle$

root(a + b)

$\sqrt[n]{a+b}$

standard deviation

$\sigma (X)$

variance(X)

$\sigma(X)^2$

median(X)

$\mathop{\mathrm{median}}(X)$

mode(X)

$\mathop{\mathrm{mode}}(X)$

degree

$\langle X^{3}\rangle$

vector

$\left(\begin{array}{c}1\\ 2\\ 3\\ x\end{array}\right)$

matrix

$\begin{pmatrix}0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 1 & 0 & 0 & 0\end{pmatrix}$

determinant

$\det A$

transpose

$A^T$

semantics

$\sin x + 5$

limit

$\lim_{x\to 0}\sin x$

symbol check

$4.56+4.56+4/5+4+5i+4.56e^{i 4.56}+\pi +e+e+i+i+\gamma +\infty +\infty$

multiset

$\{4.56, 4.56, 4/5, 4+5i, 4.56e^{i 4.56}, \pi , e, e, i, i, \gamma , \infty , \infty \}$

tendsto type = "above" with <reln>

$(x^{2}, a^{2})$

tendsto type = "above" with <apply>

$x^{2}\to a^{2}$

tendsto type = "below" with <reln>

$(x^{2}, a^{2})$

tendsto type = "below" with <apply>

$x^{2}\to a^{2}$

tendsto type = "two-sided" with <reln>

$(x^{2}, a^{2})$

tendsto type = "two-sided" with <apply>

$x^{2}\to a^{2}$

type check

$x+x+x+y+\theta +v+\pi +e+e+i+i+\gamma +\infty +\infty$

sin + cos

$\sin x+\cos x$

f(x)

$f(x)$

Source Code:

<p>a + b - c
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<ci>a</ci>
<apply>
<minus/>
<ci>b</ci>
<ci>c</ci>
</apply>
</apply>
[/itex]
</p>
<p>
x + yz + z
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<ci>x</ci>
<apply>
<times/>
<ci>y</ci>
<ci>z</ci>
</apply>
<ci>z</ci>
</apply>
[/itex]
</p>
<p>
x * (y + z) * z
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci>x</ci>
<apply>
<plus/>
<ci>y</ci>
<ci>z</ci>
</apply>
<ci>z</ci>
</apply>
[/itex]
</p>
<p>
sin(a + b)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<sin/>
<apply>
<plus/>
<ci>a</ci>
<ci>b</ci>
</apply>
</apply>
[/itex]
</p>
<p>
sin(x(y + z)z)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<sin/>
<apply>
<times/>
<ci>x</ci>
<apply>
<plus/>
<ci>y</ci>
<ci>z</ci>
</apply>
<ci>z</ci>
</apply>
</apply>
[/itex]
</p>
<p>
sin(xy)2b
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<apply>
<sin/>
<apply>
<times/>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<cn>2</cn>
<ci>b</ci>
</apply>
</apply>
[/itex]
</p>
<p>
(x + y) ^ (n - 3)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<power/>
<apply>
<plus/>
<ci>x</ci>
<ci>y</ci>
</apply>
<apply>
<minus/>
<cn>n</cn>
<cn>3</cn>
</apply>
</apply>
[/itex]
</p>
<p>
limit as x goes to a of sin x using &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<limit/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<tendsto type='above'/>
<ci>x</ci>
<ci>a</ci>
</reln>
</condition>
<apply>
<sin/>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
limit as x goes to a of sin x using &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<limit/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<apply>
<tendsto type='above'/>
<ci>x</ci>
<ci>a</ci>
</apply>
</condition>
<apply>
<sin/>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
limit as x goes to a of sin(x + y) using &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<limit/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<tendsto type='above'/>
<ci>x</ci>
<ci>a</ci>
</reln>
</condition>
<apply>
<sin/>
<apply>
<plus/>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
[/itex]
</p>
<p>
limit as x goes to a of sin(x + y) using &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<limit/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<apply>
<tendsto type='above'/>
<ci>x</ci>
<ci>a</ci>
</apply>
</condition>
<apply>
<sin/>
<apply>
<plus/>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
[/itex]
</p>
<p>
limit as x goes to a of sin(x + y)2b using &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<limit/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<tendsto type='above'/>
<ci>x</ci>
<ci>a</ci>
</reln>
</condition>
<apply>
<times/>
<apply>
<sin/>
<apply>
<times/>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<cn>2</cn>
<ci>b</ci>
</apply>
</apply>
</apply>
[/itex]
</p>
<p>
limit as x goes to a of sin(x + y)2b using &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<limit/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<apply>
<tendsto type='above'/>
<ci>x</ci>
<ci>a</ci>
</apply>
</condition>
<apply>
<times/>
<apply>
<sin/>
<apply>
<times/>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
<apply>
<times/>
<cn>2</cn>
<ci>b</ci>
</apply>
</apply>
</apply>
[/itex]
</p>
<p>
quotient
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<quotient/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
moment
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<moment/>
<degree>
<cn>3</cn>
</degree>
<ci>X</ci>
</apply>
[/itex]
</p>
<p>
selector
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<selector/>
<matrix>
<matrixrow>
<cn>1</cn>
<cn>2</cn>
</matrixrow>
<matrixrow>
<cn>3</cn>
<cn>4</cn>
</matrixrow>
</matrix>
<cn>1</cn>
</apply>
[/itex]
</p>
<p>
factorial
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<factorial/>
<ci>n</ci>
</apply>
[/itex]
</p>
<p>
(a + b)!
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<factorial/>
<apply>
<plus/>
<apply>
<plus/>
<ci>n</ci>
<ci>m</ci>
</apply>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
inverse function
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<inverse/>
<ci>f</ci>
</apply>
[/itex]
</p>
<p>
inverse matrix
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<apply>
<inverse/>
<ci type='matrix'>a</ci>
</apply>
<ci>A</ci>
</apply>
[/itex]
</p>
<p>
conjugate
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<apply>
<conjugate/>
<apply>
<plus/>
<ci>x</ci>
<apply>
<times/>
<cn>&ImaginaryI;</cn>
<ci>y</ci>
</apply>
</apply>
</apply>
</mrow>
[/itex]
</p>
<p>
a + b + c
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<ci>a</ci>
<ci>b</ci>
<ci>c</ci>
</apply>
[/itex]
</p>
<p>
integral (a + x)dx
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<int/>
<bvar>
<ci>x</ci>
</bvar>
<lowlimit>
<cn>0</cn>
</lowlimit>
<uplimit>
<ci>a</ci>
</uplimit>
<apply>
<plus/>
<ci>a</ci>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
-1 + 7
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<apply>
<minus/>
<cn>1</cn>
</apply>
<cn>7</cn>
</apply>
[/itex]
</p>
<p>
7 + (-1)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<cn>7</cn>
<apply>
<minus/>
<cn>1</cn>
</apply>
</apply>
[/itex]
</p>
<p>
max
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<max/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<apply>
<and/>
<reln>
<gt/>
<ci>x</ci>
<cn>0</cn>
</reln>
<reln>
<lt/>
<ci>x</ci>
<cn>1</cn>
</reln>
</apply>
</condition>
<apply>
<minus/>
<ci>x</ci>
<apply>
<sin/>
<ci>x</ci>
</apply>
</apply>
</apply>
[/itex]
</p>
<p>
lambda sin(x + 1)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<lambda>
<bvar>
<ci>x</ci>
</bvar>
<apply>
<sin/>
<apply>
<plus/>
<ci>x</ci>
<cn>1</cn>
</apply>
</apply>
</lambda>
[/itex]
</p>
<p>
lambda integral f(x)dx
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<lambda>
<bvar>
<ci>b</ci>
</bvar>
<apply>
<int/>
<bvar>
<ci>x</ci>
</bvar>
<lowlimit>
<ci>a</ci>
</lowlimit>
<uplimit>
<ci>b</ci>
</uplimit>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
</lambda>
[/itex]
</p>
<p>
compose f and g
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<compose/>
<fn>
<ci>f</ci>
</fn>
<fn>
<ci>g</ci>
</fn>
</apply>
[/itex]
</p>
<p>
compose f and g (x)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<apply>
<compose/>
<fn>
<ci>f</ci>
</fn>
<fn>
<ci>g</ci>
</fn>
</apply>
<ci>x</ci>
</apply>
[/itex]
</p>
<p>
f(g(x))
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<fn>
<ci>f</ci>
</fn>
<apply>
<fn>
<ci>g</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
composition of f and inverse of f eq identity using &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<eq/>
<apply>
<compose/>
<fn>
<ci>f</ci>
</fn>
<apply>
<inverse/>
<fn>
<ci>f</ci>
</fn>
</apply>
</apply>
<ident/>
</reln>
[/itex]
</p>
<p>
composition of f and inverse of f eq identity using &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<compose/>
<fn>
<ci>f</ci>
</fn>
<apply>
<inverse/>
<fn>
<ci>f</ci>
</fn>
</apply>
</apply>
<ident/>
</apply>
[/itex]
</p>
<p>
e^x
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<exp/>
<ci>x</ci>
</apply>
[/itex]
</p>
<p>
min(x, x not in B, x^2) using &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<min/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<notin/>
<ci>x</ci>
<ci type='set'>B</ci>
</reln>
</condition>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
</apply>
[/itex]
</p>
<p>
min(x, x not in B, x^2) using &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<min/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<apply>
<notin/>
<ci>x</ci>
<ci type='set'>B</ci>
</apply>
</condition>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
</apply>
[/itex]
</p>
<p>
a mod (b)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<rem/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
ab
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<times/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
gcd(a b, c)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<gcd/>
<ci>a</ci>
<ci>b</ci>
<ci>c</ci>
</apply>
[/itex]
</p>
<p>
integral
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<int/>
<bvar>
<ci>x</ci>
</bvar>
<lowlimit>
<cn>0</cn>
</lowlimit>
<uplimit>
<ci>a</ci>
</uplimit>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
abs(x)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<abs/>
<ci>x</ci>
</apply>
[/itex]
</p>
<p> tall abs(x)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<abs/>
<apply>
<divide/>
<ci>H</ci>
<ci>K</ci>
</apply>
</apply>
[/itex]
</p>
<p>
abs(x + y + z)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<abs/>
<apply>
<plus/>
<ci>x</ci>
<ci>y</ci>
<ci>z</ci>
</apply>
</apply>
[/itex]
</p>
<p>
x &gt; 0 and z &lt; 1 as &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<and/>
<reln>
<gt/>
<ci>x</ci>
<cn>0</cn>
</reln>
<reln>
<lt/>
<ci>x</ci>
<cn>1</cn>
</reln>
</apply>
[/itex]
</p>
<p>
x &gt; 0 and z &lt; 1 as &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<and/>
<apply>
<gt/>
<ci>x</ci>
<cn>0</cn>
</apply>
<apply>
<lt/>
<ci>x</ci>
<cn>1</cn>
</apply>
</apply>
[/itex]
</p>
<p>
a and b
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<and/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a or b
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<or/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a xor b
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<xor/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a eq b with &lt;reln&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<eq/>
<ci>a</ci>
<ci>b</ci>
</reln>
[/itex]
</p>
<p>
a eq b with &lt;apply&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a neq b with &lt;reln&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<neq/>
<ci>a</ci>
<ci>b</ci>
</reln>
[/itex]
</p>
<p>
a neq b with &lt;apply&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<neq/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a &gt; b with &lt;reln&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<gt/>
<ci>a</ci>
<ci>b</ci>
</reln>
[/itex]
</p>
<p>
a &gt; b with &lt;apply&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<gt/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a &lt; b with &lt;reln&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<lt/>
<ci>a</ci>
<ci>b</ci>
</reln>
[/itex]
</p>
<p>
a &lt; b with &lt;apply&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<lt/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a &lt;= b with &lt;reln&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<geq/>
<ci>a</ci>
<ci>b</ci>
</reln>
[/itex]
</p>
<p>
a &gt;= b with &lt;apply&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<geq/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
a &lt;= b with &lt;reln&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<leq/>
<ci>a</ci>
<ci>b</ci>
</reln>
[/itex]
</p>
<p>
a &lt;= b with &lt;apply&gt; tag
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<leq/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
set: {b, a, c}
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<set>
<ci>b</ci>
<ci>a</ci>
<ci>c</ci>
</set>
[/itex]
</p>
<p>
set with condition
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<set>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<lt/>
<ci>x</ci>
<cn>5</cn>
</reln>
</condition>
</set>
[/itex]
</p>
<p>
list: {b, a, c}
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<list>
<ci>b</ci>
<ci>a</ci>
<ci>c</ci>
</list>
[/itex]
</p>
<p>
list: {x|x &lt; 5}
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<list order='numeric'>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<lt/>
<ci>x</ci>
<cn>5</cn>
</reln>
</condition>
</list>
[/itex]
</p>
<p>
A union B
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<union/>
<ci>A</ci>
<ci>B</ci>
</apply>
[/itex]
</p>
<p>
A intersect B
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<intersect/>
<ci type='set'>A</ci>
<ci type='set'>B</ci>
</apply>
[/itex]
</p>
<p>
A intersect (B union C)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<intersect/>
<ci type='set'>A</ci>
<apply>
<union/>
<ci type='set'>B</ci>
<ci type='set'>C</ci>
</apply>
</apply>
[/itex]
</p>
<p>integral
x in R as &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<in/>
<ci>x</ci>
<ci type='set'>R</ci>
</reln>
[/itex]
</p>
<p>
x in R as &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<in/>
<ci>x</ci>
<ci type='set'>R</ci>
</apply>
[/itex]
</p>
<p>
a in A
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<in/>
<ci>a</ci>
<ci type='set'>A</ci>
</reln>
[/itex]
</p>
<p>
a not in A as &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<notin/>
<ci>a</ci>
<ci>A</ci>
</reln>
[/itex]
</p>
<p>
a not in A as &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<notin/>
<ci>a</ci>
<ci>A</ci>
</apply>
[/itex]
</p>
<p>
not a
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<not/>
<ci>a</ci>
</apply>
[/itex]
</p>
<p>
not (a and b)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<not/>
<apply>
<and/>
<ci>a</ci>
<ci>b</ci>
</apply>
</apply>
[/itex]
</p>
<p>
A -&gt; B (reln)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<implies/>
<ci>A</ci>
<ci>B</ci>
</reln>
[/itex]
</p>
<p>
A -&gt; B (apply)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<implies/>
<ci>A</ci>
<ci>B</ci>
</apply>
[/itex]
</p>
<p>
forall
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<forall/>
<bvar>
<ci>x</ci>
</bvar>
<reln>
<eq/>
<apply>
<minus/>
<ci>x</ci>
<ci>x</ci>
</apply>
<cn>0</cn>
</reln>
</apply>
[/itex]
</p>
<p>
forall/and/lt/power
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<forall/>
<bvar>
<ci>p</ci>
</bvar>
<bvar>
<ci>q</ci>
</bvar>
<condition>
<apply>
<and/>
<reln>
<in/>
<ci>p</ci>
<ci type='set'>Q</ci>
</reln>
<reln>
<in/>
<ci>q</ci>
<ci type='set'>Q</ci>
</reln>
<reln>
<lt/>
<ci>p</ci>
<ci>q</ci>
</reln>
</apply>
</condition>
<reln>
<lt/>
<ci>p</ci>
<apply>
<power/>
<ci>q</ci>
<cn>2</cn>
</apply>
</reln>
</apply>
[/itex]
</p>
<p>
forall/exists/and/plus
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<forall/>
<bvar>
<ci>n</ci>
</bvar>
<condition>
<apply>
<and/>
<reln>
<in/>
<ci>n</ci>
<ci type='set'>Z</ci>
</reln>
<reln>
<gt/>
<ci>n</ci>
<cn>0</cn>
</reln>
</apply>
</condition>
<apply>
<exists/>
<bvar>
<ci>x</ci>
</bvar>
<bvar>
<ci>y</ci>
</bvar>
<bvar>
<ci>z</ci>
</bvar>
<condition>
<apply>
<and/>
<reln>
<in/>
<ci>x</ci>
<ci type='set'>Z</ci>
</reln>
<reln>
<in/>
<ci>y</ci>
<ci type='set'>Z</ci>
</reln>
<reln>
<in/>
<ci>z</ci>
<ci type='set'>Z</ci>
</reln>
</apply>
</condition>
<reln>
<eq/>
<apply>
<plus/>
<apply>
<power/>
<ci>x</ci>
<ci>n</ci>
</apply>
<apply>
<power/>
<ci>y</ci>
<ci>n</ci>
</apply>
</apply>
<apply>
<power/>
<ci>z</ci>
<ci>n</ci>
</apply>
</reln>
</apply>
</apply>
[/itex]
</p>
<p>
exists
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<exists/>
<bvar>
<ci>x</ci>
</bvar>
<reln>
<eq/>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
<cn>0</cn>
</reln>
</apply>
[/itex]
</p>
<p>
forall/exists/and/plus
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<forall/>
<bvar>
<ci>n</ci>
</bvar>
<condition>
<apply>
<and/>
<reln>
<in/>
<ci>n</ci>
<ci type='set'>Z</ci>
</reln>
<reln>
<gt/>
<ci>n</ci>
<cn>0</cn>
</reln>
</apply>
</condition>
<apply>
<exists/>
<bvar>
<ci>x</ci>
</bvar>
<bvar>
<ci>y</ci>
</bvar>
<bvar>
<ci>z</ci>
</bvar>
<condition>
<apply>
<and/>
<reln>
<in/>
<ci>x</ci>
<ci type='set'>Z</ci>
</reln>
<reln>
<in/>
<ci>y</ci>
<ci type='set'>Z</ci>
</reln>
<reln>
<in/>
<ci>z</ci>
<ci type='set'>Z</ci>
</reln>
</apply>
</condition>
<reln>
<eq/>
<apply>
<plus/>
<apply>
<power/>
<ci>x</ci>
<ci>n</ci>
</apply>
<apply>
<power/>
<ci>y</ci>
<ci>n</ci>
</apply>
</apply>
<apply>
<power/>
<ci>z</ci>
<ci>n</ci>
</apply>
</reln>
</apply>
</apply>
[/itex]
</p>
<p>
ln a
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<ln/>
<ci>a</ci>
</apply>
[/itex]
</p>
<p>
log base 3 of x
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<log/>
<logbase>
<cn>3</cn>
</logbase>
<ci>x</ci>
</apply>
[/itex]
</p>
<p>
integer
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<int/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<in/>
<ci>x</ci>
<ci type='set'>D</ci>
</reln>
</condition>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
diff
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<diff/>
<bvar>
<ci>x</ci>
</bvar>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
partialdiff
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<partialdiff/>
<bvar>
<ci>x</ci>
<degree>
<cn>2</cn>
</degree>
</bvar>
<bvar>
<ci>y</ci>
</bvar>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
[/itex]
</p>
<p>
integral
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<int/>
<bvar>
<ci>x</ci>
</bvar>
<lowlimit>
<ci>a</ci>
</lowlimit>
<uplimit>
<ci>b</ci>
</uplimit>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
partialdiff
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<partialdiff/>
<bvar>
<ci>x</ci>
<degree>
<ci>n</ci>
</degree>
</bvar>
<bvar>
<ci>y</ci>
<degree>
<ci>m</ci>
</degree>
</bvar>
<apply>
<sin/>
<apply>
<times/>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
[/itex]
</p>
<p>
divide
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<divide/>
<ci>a</ci>
<ci>b</ci>
</apply>
[/itex]
</p>
<p>
divide/plus/minus
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<divide/>
<apply>
<plus/>
<ci>a</ci>
<ci>b</ci>
</apply>
<apply>
<minus/>
<ci>a</ci>
<ci>b</ci>
</apply>
</apply>
[/itex]
</p>
<p>
divide/plus/divide
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<divide/>
<apply>
<plus/>
<ci>a</ci>
<ci>b</ci>
</apply>
<apply>
<divide/>
<ci>a</ci>
<ci>b</ci>
</apply>
</apply>
[/itex]
</p>
<p>
A is subset of B as &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<subset/>
<ci>A</ci>
<ci>B</ci>
</reln>
[/itex]
</p>
<p>
A is subset of B as &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<subset/>
<ci>A</ci>
<ci>B</ci>
</apply>
[/itex]
</p>
<p>
A is proper subset of B as &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<prsubset/>
<ci>A</ci>
<ci>B</ci>
</reln>
[/itex]
</p>
<p>
A is proper subset of B as &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<prsubset/>
<ci>A</ci>
<ci>B</ci>
</apply>
[/itex]
</p>
<p>
A is not subset of B as &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<notsubset/>
<ci>A</ci>
<ci>B</ci>
</reln>
[/itex]
</p>
<p>
A is not subset of B as &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<notsubset/>
<ci>A</ci>
<ci>B</ci>
</apply>
[/itex]
</p>
<p>
A is not proper subset of B as &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<notprsubset/>
<ci>A</ci>
<ci>B</ci>
</reln>
[/itex]
</p>
<p>
A is not proper subset of B as &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<notprsubset/>
<ci>A</ci>
<ci>B</ci>
</apply>
[/itex]
</p>
<p>
Set difference
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<setdiff/>
<ci>A</ci>
<ci>B</ci>
</apply>
[/itex]
</p>
<p>
Log base 3 of x + y
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<log/>
<logbase>
<cn>3</cn>
</logbase>
<apply>
<plus/>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
[/itex]
</p>
<p>
Sum as x goes from a to b of f(x)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<sum/>
<bvar>
<ci>x</ci>
</bvar>
<lowlimit>
<ci>a</ci>
</lowlimit>
<uplimit>
<ci>b</ci>
</uplimit>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
sum
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<sum/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<in/>
<ci>x</ci>
<ci type='set'>B</ci>
</reln>
</condition>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
product
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<product/>
<bvar>
<ci>x</ci>
</bvar>
<lowlimit>
<ci>a</ci>
</lowlimit>
<uplimit>
<ci>b</ci>
</uplimit>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
product
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<product/>
<bvar>
<ci>x</ci>
</bvar>
<condition>
<reln>
<in/>
<ci>x</ci>
<ci type='set'>B</ci>
</reln>
</condition>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
tendsto with &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<tendsto type='above'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</reln>
[/itex]
</p>
<p>
tendsto with &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<tendsto type='above'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</apply>
[/itex]
</p>
<p>
tendsto with &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<tendsto/>
<vector>
<ci>x</ci>
<ci>y</ci>
</vector>
<vector>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
<ci>y</ci>
</apply>
<apply>
<fn>
<ci>g</ci>
</fn>
<ci>x</ci>
<ci>y</ci>
</apply>
</vector>
</reln>
[/itex]
</p>
<p>
tendsto with &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<tendsto/>
<vector>
<ci>x</ci>
<ci>y</ci>
</vector>
<vector>
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
<ci>y</ci>
</apply>
<apply>
<fn>
<ci>g</ci>
</fn>
<ci>x</ci>
<ci>y</ci>
</apply>
</vector>
</apply>
[/itex]
</p>
<p>
mean(X)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<mean/>
<ci>X</ci>
</apply>
[/itex]
</p>
<p>
root(a + b)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<root/>
<degree>
<ci>n</ci>
</degree>
<apply>
<plus/>
<ci>a</ci>
<ci>b</ci>
</apply>
</apply>
[/itex]
</p>
<p>
standard deviation
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<sdev/>
<ci>X</ci>
</apply>
[/itex]
</p>
<p>
variance(X)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<variance/>
<ci>X</ci>
</apply>
[/itex]
</p>
<p>
median(X)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<median/>
<ci>X</ci>
</apply>
[/itex]
</p>
<p>
mode(X)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<mode/>
<ci>X</ci>
</apply>
[/itex]
</p>
<p>
degree
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<moment/>
<degree>
<cn>3</cn>
</degree>
<ci>X</ci>
</apply>
[/itex]
</p>
<p>
vector
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<vector>
<cn>1</cn>
<cn>2</cn>
<cn>3</cn>
<ci>x</ci>
</vector>
[/itex]
</p>
<p>
matrix
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<matrix>
<matrixrow>
<cn>0</cn>
<cn>1</cn>
<cn>0</cn>
<cn>0</cn>
</matrixrow>
<matrixrow>
<cn>0</cn>
<cn>0</cn>
<cn>1</cn>
<cn>0</cn>
</matrixrow>
<matrixrow>
<cn>1</cn>
<cn>0</cn>
<cn>0</cn>
<cn>0</cn>
</matrixrow>
</matrix>
[/itex]
</p>
<p>
determinant
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<determinant/>
<ci type='matrix'>A</ci>
</apply>
[/itex]
</p>
<p>
transpose
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<transpose/>
<ci type='matrix'>A</ci>
</apply>
[/itex]
</p>
<p>
semantics
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<apply>
<plus/>
<apply>
<sin/>
<ci>x</ci>
</apply>
<cn>5</cn>
</apply>
<annotation encoding='TeX'>\sin x + 5
</annotation>
</semantics>
[/itex]
</p>
<p>
limit
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<limit/>
<bvar>
<ci>x</ci>
</bvar>
<lowlimit>
<cn>0</cn>
</lowlimit>
<apply>
<sin/>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
symbol check
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<cn type='real'>4.56</cn>
<cn type='integer'>4.56</cn>
<cn type='rational'>4
<sep/>5
</cn>
<cn type='complex-cartesian'>4
<sep/>5
</cn>
<cn type='complex-polar'>4.56
<sep/>4.56
</cn>
<cn type='constant'>&pi;</cn>
<cn>&ExponentialE;</cn>
<cn>&ee;</cn>
<cn>&ImaginaryI;</cn>
<cn>&ii;</cn>
<cn>&gamma;</cn>
<cn>&infin;</cn>
<cn>&infin;</cn>
</apply>
[/itex]
</p>
<p>
multiset
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<set type='multiset'>
<cn type='real'>4.56</cn>
<cn type='integer'>4.56</cn>
<cn type='rational'>4
<sep/>5
</cn>
<cn type='complex-cartesian'>4
<sep/>5
</cn>
<cn type='complex-polar'>4.56
<sep/>4.56
</cn>
<cn type='constant'>&pi;</cn>
<cn>&ExponentialE;</cn>
<cn>&ee;</cn>
<cn>&ImaginaryI;</cn>
<cn>&ii;</cn>
<cn>&gamma;</cn>
<cn>&infin;</cn>
<cn>&infin;</cn>
</set>
[/itex]
</p>
<p>
tendsto type = "above" with &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<tendsto type='above'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</reln>
[/itex]
</p>
<p>
tendsto type = "above" with &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<tendsto type='above'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</apply>
[/itex]
</p>
<p>
tendsto type = "below" with &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<tendsto type='below'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</reln>
[/itex]
</p>
<p>
tendsto type = "below" with &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<tendsto type='below'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</apply>
[/itex]
</p>
<p>
tendsto type = "two-sided" with &lt;reln&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<reln>
<tendsto type='two-sided'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</reln>
[/itex]
</p>
<p>
tendsto type = "two-sided" with &lt;apply&gt;
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<tendsto type='two-sided'/>
<apply>
<power/>
<ci>x</ci>
<cn>2</cn>
</apply>
<apply>
<power/>
<ci>a</ci>
<cn>2</cn>
</apply>
</apply>
[/itex]
</p>
<p>
type check
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<ci type='real'>x</ci>
<ci type='integer'>x</ci>
<ci type='rational'>x</ci>
<ci type='complex-cartesian'>y</ci>
<ci type='complex-polar'>&theta;</ci>
<ci type='vector'>v</ci>
<ci type='constant'>&pi;</ci>
<ci>&ExponentialE;</ci>
<ci>&ee;</ci>
<ci>&ImaginaryI;</ci>
<ci>&ii;</ci>
<ci>&gamma;</ci>
<ci>&infin;</ci>
<ci>&infin;</ci>
</apply>
[/itex]
</p>
<p>
sin + cos
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<plus/>
<apply>
<sin/>
<ci>x</ci>
</apply>
<apply>
<cos/>
<ci>x</ci>
</apply>
</apply>
[/itex]
</p>
<p>
f(x)
<br />
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<fn>
<ci>f</ci>
</fn>
<ci>x</ci>
</apply>
[/itex]
</p>