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This is a list of mathematical symbols and expressions used on Asphalt Wiki.

As the list is meant for players not familiar with a certain symbol or expression, the following table is sorted by symbols, not by their meanings.

• Symbols are sorted under !$@. They may sometimes contain additional grey variables for clarity reasons, like$ {\color{grey}n}! $or$ \{{\color{grey}a}, {\color{grey}b}\} $. • Symbols that resemble letters are listed both under !$@ and the corresponding letter.
• Expressions that are commonly used with specific 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 !$@ because its main elements are brackets, but not under B for "binomial coefficient". • Greek letters can be found under !$@ as well as under their Latin equivalents.

#### !$@ Basic symbols$ a^b $Exponentiation (for numbers)$ a^b = \underbrace{a \cdot a \cdot \ldots \cdot a}_{b\, \mathrm{times}} $read: "$ a $raised to the power of$ b $" or most briefly: "$ a $to the$ b $"$ 2^A $Alternative notation for the →power set of$ A $(for sets)$ {\color{grey}a}\cdot{\color{grey}b} $Multiplication$ a \cdot b $read: "$ a $times$ b $" (preferred to$ \times $in mathematical contexts on this wiki to avoid confusion with the letter x)$ {\color{grey}n}! $Factorial of$ n  5! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5  \sim $Has the probability distribution (for random variables)$ X \sim D $read: "$ X $has (the probability) distribution$ D $." or: "$ X $is$ D $-distributed."$ \approx $Approximately equal to (for numbers)$ \frac23 \approx 0.67 $read: "Two thirds is approximately equal to 0.67."$ \infty $Infinity Symbols pointing in a direction$ <  > $Less than Greater than$ a < b $read: "$ a $is less than$ b $." ($ a $is not equal to$ b $.)$ \subset  \supset $Proper (strict) subset of Proper (strict) superset of$ A \subset B $read: "$ A $is a proper subset of$ B $." ($ A $is not equal to$ B $.)$ \le  \ge $Less than or equal to Greater than or equal to$ a \le b $read: "$ a $is less than or equal to$ b $."$ \subseteq  \supseteq $Subset of or equal to Superset of or equal to$ A \subseteq B $read: "$ A $is a subset of or equal to$ B $."$ \land $And (for logical statements and equations)$ A \cap B = \{ x \mid x \in A \land x \in B\} $read: "$ A $intersected with$ B $equals the set of all$ x $such that$ x \in A $and$ x \in B $."$ \cap $Intersection (for sets)$ A \cap B = \{ x \mid x \in A \land x \in B\} $read: "$ A $intersected with$ B $equals the set of all$ x $such that$ x \in A $and$ x \in B $."$ \lor $Or (for logical statements and equations)$ x^2 = 9 \iff x = 3 \lor x = -3 $read: "$ x^2 $equals$ 9 $if and only if$ x = 3 $or$ x = -3 $."$ \cup $Union (for sets)$ A \cup B = \{ x \mid x \in A \lor x \in B\} $read: "The union of$ A $and$ B $equals the set of all$ x $such that$ x \in A $or$ x \in B $."$ \to $Approaches$ \overline{X}_n \, \to \, \mu \ \ \mathrm{when}\ \ n \to \infty $read: "$ X_n $bar approaches$ \mu $when$ n $approaches infinity."$ \xrightarrow{{\color{grey}\mathrm{a.\ s.}}} $Almost sure convergence$ \xrightarrow{{\color{grey}\mathrm P}} $Convergence in probability$ \Rightarrow $Implication (for logical statements and equations)$ x = 3 \Rightarrow x^2 = 9 $read: "implies" (It follows from$ x = 3 $that$ x^2 = 9 $, but it doesn't follow from$ x^2 = 9 $that$ x = 3 $since$ x $could also be$ -3 $.)$ \iff $Equivalence (for logical statements and equations)$ 2x = 10 \iff x = 5 $read: "if and only if" (Both statements imply each other.) Brackets$ ({\color{grey}a}, {\color{grey}b}) $1. Tuple (An$ n $-tuple is an ordered list of$ n $elements.$ (a, b) $is not the same as$ (b, a) $.) 2. Alternative notation for the →open interval$ \mathopen{]}a,b\mathclose{[}  (a, b, c) $read: "the 3-tuple (triple) of$ a, b, c $"$ \binom{{\color{grey}n}}{{\color{grey}k}} $Binomial coefficient$ [{\color{grey}a}, {\color{grey}b}] $Closed interval from$ a $to$ b $(including$ a $and$ b $)$ \mathopen{[}a,b\mathclose{]} = \{x \in \R \mid a \le x \le b \}  ]{\color{grey}a}, {\color{grey}b}[ $Open interval from$ a $to$ b $(excluding$ a $and$ b $)$ \mathopen{]}a,b\mathclose{[} = \{x \in \R \mid a < x < b \} $(preferred to$ (a, b) $on this wiki to avoid confusion with the →tuple$ (a, b) $)$ \{\} $Empty set$ \{{\color{grey}a}, {\color{grey}b}\} $Set (unordered,$ \{a, b\} $is the same as$ \{b, a\} $)$ \{a, b, c\} $read: "the set of$ a $,$ b $, and$ c $"$ \{ {\color{grey}x} \mid {\color{grey}A(x)}\} $Set-builder notation (the set of all$ x $for which$ A(x) $is true)$ \{x \in \N \mid x < 5 \} = \{1, 2, 3, 4\} $read: "the set of all$ x $that are elements of$ \N $such that$ x < 5 $" Bars$ {\color{grey}1.}\bar{\color{grey}{3}} $Repeating decimal$ 1.\bar3 = 1.3333\dots $read: "one point three repeating"$ \bar{\color{grey}{x}} $Arithmetic mean$ \bar{\color{grey}A} $Complementary event read: "$ A $bar"$ {\color{grey}\mathrm{P}(A} \mid {\color{grey}B)} $Conditional probability$ {\color{grey}\{x} \mid {\color{grey}A(x)\}} $Set-builder notation$ |{\color{grey}a}| $Absolute value of$ a $(for numbers, the non-negative value of$ a $without regard to its sign)$ |-2| = 2  |{\color{grey}A}| $Cardinality of$ A $(for sets, the number of elements in the set$ A $)$ |A| = 4  \lfloor {\color{grey}a} \rfloor $Floor function (for numbers, the greatest integer less than or equal to$ a $)$ \lfloor 2.8 \rfloor = 2 $read: "floor of 2.8"$ \lceil {\color{grey}a} \rceil $Ceiling function (for numbers, the least integer greater than or equal to$ a $)$ \lceil 2.2 \rceil = 3 $read: "ceiling of 2.2" Letter-based symbols$ \forall $For all$ \in $Element of$ \varnothing $Empty set$ \varepsilon $Epsilon (lower case)$ \mu $Mu (lower case)$ \omega $Omega (lower case)$ \Omega $Omega (upper case)$ \Pi $Pi (upper case)$ \sigma $Sigma (lower case)$ \sigma^2 $Sigma² (lower case)$ \Sigma $Sigma (upper case) #### A$ \land $And$ \forall $For all$ x+x=2x \; \forall x \in \R $read: "$ x+x=2x $for all$ x $in$ \R $."$ \mathrm{a. s.} $Almost surely$ \xrightarrow{\mathrm{a.\ s.}} $Almost sure convergence$ {X_n \, \xrightarrow{\mathrm{a.\ s.}} \, X} $read: "$ X_n $converges almost surely towards$ X $." #### B$ \mathrm{B}(n, p) $Binomial distribution$ X \sim \mathrm{B}(n, p) $read: "$ X $is binomially distributed with parameters$ n $and$ p $."$ \mathrm{Ber}(p) $Bernoulli distribution, also written as$ \mathrm{Bernoulli}(p)  X \sim \mathrm{Ber}(p) $read: "$ X $is Bernoulli distributed with parameter$ p $." #### E$ e $The mathematical constant$ e $($ \approx 2.71828 $)$ e = \displaystyle\lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n  \operatorname{E}[X] $Expected value read: "Expected value of$ X $"$ \varepsilon $Epsilon (Greek, lower case): often used to denote an arbitrarily small positive quantity, particularly for the definition of a →limit$ \in $Element of$ x \in \R $read: "$ x $is an element of$ \R $."$ \Sigma $Sigma (upper case) #### I$ \mathrm{i. i. d.} $Independent and identically distributed #### L$ \mathrm{lim} $Limit (a value that a sequence or function "tends to")$ \displaystyle\lim_{n\to\infty}0.3^n = 0 $read: "the limit of$ 0.3^n $, as$ n $approaches infinity"$ \ln x $Natural logarithm (The natural logarithm of$ x $is the power to which →e would have to be raised to equal$ x $.)$ \ln e^x = x $#### M$ \mu $Mu (Greek, lower case): population mean, also used for →expected value read: "mew" [mjuː] #### N$ \N $The set of natural numbers$ \binom{n}{k} $Binomial coefficient$ \binom{n}{k} = \frac{n!}{k! (n-k)!} $read: "n choose k" #### O$ \varnothing $Empty set$ \varnothing = \{\} $(The symbol was actually derived from the letter Ø in the Norwegian alphabet.)$ \omega $Omega (Greek, lower case): element of a sample space$ \Omega $Omega (Greek, upper case): sample space #### P$ \mathrm P(A) $Probability (for events) read: "the probability of$ A $"$ \mathcal P(A) $Power set (for sets, the set of all →subsets of$ A $, including the →empty set and$ A $itself)$ \mathcal P(A) = 2^A $read: "the power set of$ A $" •$ \mathcal P $is written in calligraphy typeface to avoid confusion with the →probability$ \mathrm P(A) $. • If$ |A| = n $, then$ |\mathcal P(A)| = 2^n $, which is the motivation for the alternative notation$ 2^A $.$ \mathrm{P}(A \mid B) $Conditional probability read: "the conditional probability of$ A $given$ B $" or: "the probability of$ A $under the condition$ B $"$ \xrightarrow{\mathrm P} $Convergence in probability$ {X_n \, \xrightarrow{\mathrm P} \, X} $read: "$ X_n $converges in probability towards$ X $."$ \Pi $Pi (Greek, upper case): product$ \prod_{i=1}^4 a_i = a_1\cdot a_2\cdot a_3\cdot a_4 $read: "product over$ i $from 1 to 4 of$ a_i $" or: "product , as$ i $goes from 1 to 4, of$ a_i $" #### Q$ \mathbb{Q} $The set of rational numbers #### R$ \R $The set of real numbers #### S$ s $Standard deviation of a sample$ s^2 $Variance of a sample$ \sigma $Sigma (Greek, lower case): standard deviation of a population$ \sigma^2 $Sigma (Greek, lower case, squared): variance of a population$ \Sigma $Sigma (Greek, upper case): sum$ \displaystyle\sum_{i=1}^{4} a_i = a_1 + a_2 + a_3 + a_4 $read: "sum over$ i $from 1 to 4 of$ a_i $" or: "sum, as$ i $goes from 1 to 4, of$ a_i $" #### U$ \cup $Union$ \cap $Intersection #### V$ \lor $Or$ \forall $For all$ \land $And$ \mathrm{Var}(X) $Variance of$ X $, usually denotes the population variance$ \sigma^2 $#### W$ \omega $Omega (lower case) #### X$ \bar{x} $Arithmetic mean, sample mean read: "$ x $bar" #### Z$ \Z \$ The set of integers
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