1. Both sets have a finite number of elements. The subset has
fewer elements. There are elements in the superset which are not
in the subset. Subset ~= Superset.
2. Both sets have an infinite set of discrete elements, such as
the set of integers.
3. Both sets have an infinite set of non discrete elements, such
as the set of real numbers.
In cases 2 and 3, Cantor proved long ago that these sets can be
mapped into each other. Subset = Superset in the number of elemnts
present. However there are still an infinity of elements in the
superset not in the subset. Subset still ~= Superset.
If the universe is a finite collection of digital elements, case 1
applies. If the universe is infinite, cases 2 or 3 apply.
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| Hara Ra <harara@shamanics.com> |
| Box 8334 Santa Cruz, CA 95061 |
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