Set (mathematics): Difference between revisions
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imported>Aleksander Stos m (better wording) |
imported>Larry Sanger (and logic, of course!) |
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In [[mathematics]], '''set''' refers to any collection of distinct elements. | In [[logic]] and [[mathematics]], '''set''' refers to 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. | 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. | ||
Revision as of 23:11, 29 March 2007
In logic and mathematics, set refers to 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}