Set (mathematics): Difference between revisions
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imported>Aleksander Stos m (math Wgp, of course) |
imported>Peter J. King m (tidied) |
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In [[logic]] and [[mathematics]], '''set''' | In [[logic]] and [[mathematics]], a '''set''' is any collection of distinct elements. | ||
Despite this intuitive definition, a set cannot be defined formally in terms of other mathematical objects, thus it is generally accepted that a set is an | Despite this intuitive definition, a set cannot be defined formally in terms of other mathematical objects, thus it is generally accepted that a set is an "undefined" entity. Because of this property, sets are fundamental structures in mathematics. | ||
==Notation== | ==Notation== | ||
Sets can be denoted by a list of objects separated with commas, enclosed with curly brackets. For example, {1, 2, 3} is the set of the numbers 1, 2, and 3. We say that 1, 2, and 3 are its ''members''. | Sets can be denoted by a list of objects separated with commas, enclosed with curly brackets. For example, {1, 2, 3} is the set of the numbers 1, 2, and 3. We say that 1, 2, and 3 are its ''members''. | ||
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:''A'' = {x | 1 < x < 10, x is a natural number} | :''A'' = {x | 1 < x < 10, x is a natural number} | ||
can be read as follows: A is the set of all x, where x is between 1 and 10, and x is a natural number. A could also be written as: | |||
:''A'' = {2, 3, 4, 5, 6, 7, 8, 9} | :''A'' = {2, 3, 4, 5, 6, 7, 8, 9} | ||
==See | ==See also== | ||
* [[Set theory]] | * [[Set theory]] | ||
* [[Mathematics]] | * [[Mathematics]] | ||
Revision as of 07:21, 7 April 2007
In logic and mathematics, a set is any collection of distinct elements.
Despite this intuitive definition, a set cannot be defined formally in terms of other mathematical objects, thus it is generally accepted that a set is an "undefined" entity. Because of this property, sets are fundamental structures in mathematics.
Notation
Sets can be denoted by a list of objects separated with commas, enclosed with curly brackets. For example, {1, 2, 3} is the set of the numbers 1, 2, and 3. We say that 1, 2, and 3 are its members.
There are many other ways to write out sets. For example,
- A = {x | 1 < x < 10, x is a natural number}
can be read as follows: A is the set of all x, where x is between 1 and 10, and x is a natural number. A could also be written as:
- A = {2, 3, 4, 5, 6, 7, 8, 9}