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

  • For a glossary of Asphalt-specific terms, see 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 by their meanings.

  • Symbols are sorted under !$@. They may sometimes contain additional gray variables for clarity reasons, like or .
  • Symbols that resemble letters are listed both under !$@ 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 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
Exponentiation
(for numbers)

read: " raised to the power of "
or most briefly: " to the "
Alternative notation for the →power set of
(for sets)
Multiplication
read: " times "
(preferred to in mathematical contexts on this wiki to avoid confusion with the letter x and the cross product )
Factorial of
Has the probability distribution
(for random variables)

read: " has (the probability) distribution ."
or: " is -distributed."
Approximately equal to
(for numbers)

read: "Two thirds is approximately equal to 0.67."
Is defined as; is equal by definition to
Infinity
Symbols pointing in a direction

Less than
Greater than

read: " is less than ."
( is not equal to .)

Proper (strict) subset of
Proper (strict) superset of

read: " is a proper subset of ."
( is not equal to .)

Less than or equal to
Greater than or equal to

read: " is less than or equal to ."

Subset of or equal to
Superset of or equal to

read: " is a subset of or equal to ."
And
(for logical statements and equations)

read: " intersected with equals the set of all such that and ."
Intersection
(for sets)

read: " intersected with equals the set of all such that and ."
Or
(for logical statements and equations)

read: " equals if and only if or ."
Union
(for sets)

read: "The union of and equals the set of all such that or ."
Approaches
read: " bar approaches when approaches infinity."
Almost sure convergence
Convergence in probability
Implication
(for logical statements and equations)

read: "implies"
(It follows from that , but it doesn't follow from that since could also be .)
Equivalence
(for logical statements and equations)

read: "if and only if"
(Both statements imply each other.)
Brackets
1. Tuple
(An -tuple is an ordered list of elements. is not the same as .)
2. Alternative notation for the →open interval

read: "the 3-tuple (triple) of "
Binomial coefficient
Closed interval from to
(including and )
Open interval from to
(excluding and )

(preferred to on this wiki to avoid confusion with the →tuple )
Empty set
Set
(unordered, is the same as )

read: "the set of , , and "
Set-builder notation
(the set of all for which is true)

read: "the set of all that are elements of such that "
Bars
Repeating decimal
read: "one point three repeating"
Arithmetic mean
Complementary event read: " bar"
Conditional probability
Set-builder notation
Absolute value of
(for numbers, the non-negative value of without regard to its sign)
Cardinality of
(for sets, the number of elements in the set )
Floor function
(for numbers, the greatest integer less than or equal to )

read: "floor of 2.8"
Ceiling function
(for numbers, the least integer greater than or equal to )

read: "ceiling of 2.2"
Letter-based symbols
For all
Element of
Empty set
Epsilon (lower case)
Mu (lower case)
Omega (lower case)
Omega (upper case)
Pi (upper case)
Sigma (lower case)
Sigma² (lower case)
Sigma (upper case)

A

And
For all
read: " for all in ."
Almost surely
Almost sure convergence
read: " converges almost surely towards ."

B

Binomial distribution
read: " is binomially distributed with parameters and ."
Bernoulli distribution, also written as
read: " is Bernoulli distributed with parameter ."

E

The mathematical constant
()
Expected value read: "Expected value of "
Epsilon (Greek, lower case): often used to denote an arbitrarily small positive quantity, particularly for the definition of a →limit
Element of
read: " is an element of ."
Sigma (upper case)

I

Independent and identically distributed

L

Limit
(a value that a sequence or function "tends to")

read: "the limit of , as approaches infinity"
Natural logarithm
(The natural logarithm of is the power to which →e would have to be raised to equal .)

M

Modulo operation
read: " modulo "
Mu (Greek, lower case):
population mean, also used for →expected value
read: "mew" [mjuː]

N

The set of natural numbers
Binomial coefficient
read: "n choose k"

O

Empty set
(The symbol was actually derived from the letter Ø in the Norwegian alphabet.[1])
Omega (Greek, lower case): element of a sample space
Omega (Greek, upper case): sample space

P

Probability
(for events)
read: "the probability of "
Power set
(for sets, the set of all →subsets of , including the →empty set and itself)

read: "the power set of "
  • is written in calligraphy typeface to avoid confusion with the →probability .
  • If , then , which is the motivation for the alternative notation .
Conditional probability read: "the conditional probability of given "
or: "the probability of under the condition "
Convergence in probability
read: " converges in probability towards ."
Pi (Greek, upper case): product
read: "product over from 1 to 4 of "
or: "product , as goes from 1 to 4, of "

Q

The set of rational numbers

R

The set of real numbers

S

Standard deviation of a sample
Variance of a sample
Sigma (Greek, lower case): standard deviation of a population
Sigma (Greek, lower case, squared): variance of a population
Sigma (Greek, upper case): sum
read: "sum over from 1 to 4 of "
or: "sum, as goes from 1 to 4, of "

U

Union
Intersection

V

Or
For all
And
Variance of , usually denotes the population variance

W

Omega (lower case)

X

Arithmetic mean, sample mean read: " bar"

Z

The set of integers

References

  1. Weil, André (1992). The Apprenticeship of a Mathematician. Birkhäuser Verlag. p. 114. Retrieved on 2019-07-21.