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