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4.5.  Three Fundamental Features of Sets

1.
All the elements of a set are distinct.
In other words: no element may `occur' more than once in a set. This is because an object x cannot be member of a set in more than one way. Either x is a member of S or not.

2.
The elements of a set are not ordered in any way.
To know, that x and y are members of a set cannot tell us in which order they occur.

3.
A set must be distinguished from its description.
For instance, the following expressions are clearly different:

{ 2, 3, 4 }, { 3, 2, 4 }, { 2, 2, 3, 4, 4, 4 }

{ n | 2 [lt] n [lt] 4 }, { m | 2 [lt] m [lt] 4 }, { n | 1 < n < 5 }

However, all these descriptions are equivalent: They denote the same set.


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Created by unroff & hp-tools. © by Hans-Peter Bischof. All Rights Reserved (1998).

Last modified: 27/July/98 (12:14)