## Subset

A portion of a Set. is a subset of (written ) Iff every member of is a member of . If is a Proper Subset of (i.e., a subset other than the set itself), this is written .

A Set of elements has subsets (including the set itself and the Empty Set). For sets of , 2, ... elements, the numbers of subsets are therefore 2, 4, 8, 16, 32, 64, ... (Sloane's A000079). For example, the set has the two subsets and . Similarly, the set has subsets (the Empty Set, , , and .

References

Courant, R. and Robbins, H. What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, p. 109, 1996.

Ruskey, F. ``Information of Subsets of a Set.'' http://sue.csc.uvic.ca/~cos/inf/comb/SubsetInfo.html.

Sloane, N. J. A. Sequence A000079/M1129 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.