In a pair of unanimous decisions, the court held that under California's 1959 state civil rights law, the Scouts are not a business establishment and so are free, like any private club, to set membership policies as they see fit.
32.
There are a few different symbols in use for a cyclic relation . uses concatenation : . and use ordered triples and the set membership symbol : . uses concatenation and set membership :, understanding as a cyclically ordered triple.
33.
The authors state that the use of equality operator ( " = " ) to denote set membership rather than the set membership operator ( " " " ) is an abuse of notation, but that doing so has advantages.
34.
The authors state that the use of equality operator ( " = " ) to denote set membership rather than the set membership operator ( " " " ) is an abuse of notation, but that doing so has advantages.
35.
In 2000, the Supreme Court ruled in " Boy Scouts of America v . Dale " that Boy Scouts, and all similar private voluntary organizations, have the constitutionally protected right under the First Amendment of freedom of association to set membership standards.
36.
However, Bart Kosko shows in Fuzziness vs . Probability that probability theory is a subtheory of fuzzy logic, as questions of degrees of belief in mutually-exclusive set membership in probability theory can be represented as certain cases of non-mutually-exclusive graded membership in fuzzy theory.
37.
It is sometimes possible to determine set membership in a plain list in O ( " k " ) time, in a time that is independent of the total number of keys, such as when the list is known to be in an arithmetic sequence or some other computable sequence.
38.
Like any ordinal number ( in von Neumann's approach ), ? 1 is a well-ordered set, with set membership ( " & isin; " ) serving as the order relation . ? 1 is a limit ordinal, i . e . there is no ordinal ? with ? + 1 = ? 1.
39.
We can consider operations such as equivalence ( whether two people have the same last name ), set membership ( whether a person has a name in a given list ), counting ( how many people have a given last name ), or finding the mode ( which name occurs most often ).
40.
That is, if there is a formula \ theta ( Z ) in the language of Peano arithmetic with no free number variables and a new set parameter " Z " and set membership relation \ in such that " Y " is the unique set " Z " such that \ theta ( Z ) holds.
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