## cardinal numberA number, often called simply a cardinal, that is used
to count the objects or ideas in a set or collection: zero, one, two, ...
, eighty-three, and so on. The cardinality of a set is
just the number of elements the set contains. For finite sets this is always
a natural number. To compare the
sizes of two sets, X and Y, all
that's necessary is to pair off the elements of X with those of Y
and see if there are any left over. This concept is obvious in the case
of finite sets but leads to some strange conclusions when dealing with infinite
sets (see infinity). For example, it is
possible to pair off all the natural numbers with all the even numbers,
with none left over; thus the set of natural numbers and the set of even
numbers have the same cardinality. In fact, an infinite set can be defined
as any set that has a proper subset of the same cardinality. Every countable
set that is infinite has a cardinality of aleph-null;
the set of real numbers has cardinality
aleph-one. See also ordinal number.
## Related category• TYPES OF NUMBERS | |||||

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