Help:Mathematical symbols and expressions

This is a list of mathematical symbols and expressions used on.
 * For a glossary of Asphalt-specific terms, see Asphalt Wiki:Glossary.
 * For a general FANDOM glossary, see Help:Glossary.

As the list is meant for players not familiar with a certain symbol or expression, the following table is sorted by symbols, not their meanings.
 * Expressions containing letters are sorted under the first letter that appears in them. For example, a player searching for the meaning of $$\binom{n}{k}$$ will find it under N, and also under !$@ because its main elements are brackets, but not under B for "binomial coefficient".
 * Symbols are sorted under !$@.
 * Greek letters can be found under !$@ as well as under their Latin equivalents.

{| class="wikitable" !colspan="3" style="background:;"|

!$@
!colspan="3" style="background:;"|
 * $$\in$$
 * Is an element of
 * $$\infty$$
 * Infinity
 * $$\binom{n}{k}$$
 * $$[a, b]$$
 * Closed interval from $$a$$ to $$b$$, including $$a$$ and $$b$$
 * $$|x|$$
 * Absolute value of $$x$$
 * $$|-2| = 2$$
 * $$\Omega$$
 * $$\omega$$
 * $$\Pi$$
 * $$\Sigma$$
 * $$\sigma$$
 * $$\sigma^2$$
 * $$\subset$$
 * Is a subset of
 * $$\to$$
 * Tends to
 * $$\Omega$$
 * $$\omega$$
 * $$\Pi$$
 * $$\Sigma$$
 * $$\sigma$$
 * $$\sigma^2$$
 * $$\subset$$
 * Is a subset of
 * $$\to$$
 * Tends to
 * $$\Sigma$$
 * $$\sigma$$
 * $$\sigma^2$$
 * $$\subset$$
 * Is a subset of
 * $$\to$$
 * Tends to
 * $$\sigma$$
 * $$\sigma^2$$
 * $$\subset$$
 * Is a subset of
 * $$\to$$
 * Tends to
 * $$\subset$$
 * Is a subset of
 * $$\to$$
 * Tends to
 * $$\to$$
 * Tends to
 * $$\to$$
 * Tends to

A
!colspan="3" style="background:;"|
 * $$\mathrm{a. s.}$$
 * Almost surely
 * $$\xrightarrow{\mathrm{a. s.}}$$
 * Almost sure convergence
 * $$\xrightarrow{\mathrm{a. s.}}$$
 * Almost sure convergence
 * Almost sure convergence

E
!colspan="3" style="background:;"|
 * $$\operatorname{E}[X]$$
 * Expected value of $$X$$
 * Expected value of $$X$$

I
!colspan="3" style="background:;"|
 * $$\mathrm{i. i. d.}$$
 * Independent and identically distributed
 * Independent and identically distributed

O
!colspan="3" style="background:;"|
 * $$\Omega$$
 * Omega (Greek, upper case): sample space
 * $$\omega$$
 * Omega (Greek, lower case): element of a sample space
 * $$\omega$$
 * Omega (Greek, lower case): element of a sample space
 * Omega (Greek, lower case): element of a sample space

L
!colspan="3" style="background:;"|
 * $$\mathrm{lim}$$
 * Limit (a value that a sequence or function "approaches" or "tends to")
 * $$\displaystyle\lim_{n\to\infty}0.3^n = 0$$ read: "the limit of $$0.3^n$$ as $$n$$ tends to infinity"
 * $$\displaystyle\lim_{n\to\infty}0.3^n = 0$$ read: "the limit of $$0.3^n$$ as $$n$$ tends to infinity"

N
!colspan="3" style="background:;"|
 * $$\binom{n}{k}$$
 * Binomial coefficient
 * $$\binom{n}{k} = \frac{n!}{k! (n-k)!}$$ read: "n choose k"
 * $$\binom{n}{k} = \frac{n!}{k! (n-k)!}$$ read: "n choose k"

P
!colspan="3" style="background:;"|
 * $$P(X)$$
 * Probability of $$X$$
 * $$\xrightarrow{P}$$
 * Convergence in probability
 * $$\Pi$$
 * Pi (Greek, upper case): product
 * $$\prod_{i=1}^4 a_i = a_1\cdot a_2\cdot a_3\cdot a_4$$ read: "the product, as $$i$$ goes from 1 to 4, of $$a_i$$"
 * $${\mathrm{plim}}$$
 * Convergence in probability
 * $$\Pi$$
 * Pi (Greek, upper case): product
 * $$\prod_{i=1}^4 a_i = a_1\cdot a_2\cdot a_3\cdot a_4$$ read: "the product, as $$i$$ goes from 1 to 4, of $$a_i$$"
 * $${\mathrm{plim}}$$
 * Convergence in probability
 * Convergence in probability

R
!colspan="3" style="background:;"|
 * $$\mathbb R$$
 * The set of real numbers
 * The set of real numbers

S
!colspan="3" style="background:;"|
 * $$s$$
 * Standard deviation of a sample
 * $$s^2$$
 * Variance of a sample
 * $$\Sigma$$
 * Sigma (Greek, upper case): sum
 * $$\displaystyle\sum_{i=1}^{4} a_i = a_1 + a_2 + a_3 + a_4$$ read: "the sum, as $$i$$ goes from 1 to 4, of $$a_i$$"
 * $$\sigma$$
 * Sigma (Greek, lower case): standard deviation of a population
 * $$\sigma^2$$
 * Sigma (Greek, lower case, squared): variance of a population
 * $$\displaystyle\sum_{i=1}^{4} a_i = a_1 + a_2 + a_3 + a_4$$ read: "the sum, as $$i$$ goes from 1 to 4, of $$a_i$$"
 * $$\sigma$$
 * Sigma (Greek, lower case): standard deviation of a population
 * $$\sigma^2$$
 * Sigma (Greek, lower case, squared): variance of a population
 * $$\sigma^2$$
 * Sigma (Greek, lower case, squared): variance of a population
 * Sigma (Greek, lower case, squared): variance of a population

X

 * $$\bar{x}$$
 * Arithmetic mean
 * read: "$$x$$ bar"
 * }
 * }