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Date: 13-1-2022
1492
Date: 27-12-2021
1498
Date: 16-1-2022
1345
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Given a set with a subset , the complement (denoted or ) of with respect to is defined as
(1) |
Using set difference notation, the complement is defined by
(2) |
If , then
(3) |
where is the empty set. The complement is implemented in the Wolfram Language as Complement[l, l1, ...].
Given a single set, the second probability axiom gives
(4) |
Using the fact that ,
(5) |
(6) |
This demonstrates that
(7) |
Given two sets,
(8) |
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(9) |
REFERENCES:
Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 2, 1991.
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