Database Architecture and Design

Set Theory

Under Construction

The Concept of a Set

Let us use the following (paraphrased) informal definition of a set [2STOLL]:

A set S is any collection of definite, distinguishable objects - real or imagined - to be conceived as a whole. The objects are called the elements or members of the set.

Note the word distinguishable - it is of the first order of importance. For those of you who know the meaning of the word null, or the phrase primary key it should strike an immediate chord.

Some Observations

The following are observations that relate back to first principles:

• {a,b,c} = {c,b,a} -- Order of elements is not significant.
• {a,b,c} = {a,c,c,b,a} Only Distinguishable elements are significant.
• {{a,b},{a,c}} <> {a,b,c} The first set contains tuples, the second set contains elements.

Notes

References:

[1STOLL] Stoll, Robert, Page 2 Set theory and Logic

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Updated January 27, 2005