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A definition of a term is a statement that gives the meaning of the term. For example, a definition of “sphenic number” is “a composite integer with three distinct prime factors.” A mathematical concept is well-defined if its content is independent on the form or the alternative representative which is used for defining it.
A definition of a constant is an equation with a symbol (or some other notation) on the left and either an exact value or a formula for a value on the right. For example, the definition of the golden ratio is
A definition of a function is an equation, usually with function notation on the left (a symbol, with an argument or a list of arguments in parentheses) and on the right a formula using the arguments to calculate the value of the function for those arguments. Optionally, the equation could be accompanied by statements of what acceptable arguments are. For example, Euler's totient function is defined as
for
 . To give one more example: the factorial function is defined as
for
 . Euler's gamma function  is sometimes said to extend the definition of factorials to any
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"definition" is owned by PrimeFan.
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Cross-references: Euler's gamma function, factorial function, Euler's totient function, calculate, argument, function, golden ratio, right, equation, independent, well-defined, term
There are 190 references to this entry.
This is version 2 of definition, born on 2007-09-14, modified 2007-09-14.
Object id is 9936, canonical name is Definition.
Accessed 2861 times total.
Classification:
| AMS MSC: | 00A05 (General :: General and miscellaneous specific topics :: General mathematics) |
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Pending Errata and Addenda
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