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A collection of objects, known as the elements of the set,
specified in such a way that we can tell in principle whether
or not a given object belongs to it. E.g. the set of all prime
numbers, the set of zeros of the cosine function.
For each set there is a
predicate (or property) which is
true for (posessed by) exectly those objects which are
elements of the set. The predicate may be defined by the set
or vice versa. Order and repetition of elements within the
Some common set of numbers are given the following names:
Z = the
integers ..., -2, -1, 0, 1, 2, ...
The empty set is the set with no elements. The intersection
of two sets X and Y is the set containing all the elements x
such that x is in X and x is in Y. The union of two sets is
the set containing all the elements x such that x is in X or x
is in Y.
(1995-01-24)