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The cardinality or "size" of a multiset is the sum of the multiplicities of all its elements. For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6.
HyperLogLog is an algorithm for the count-distinct problem, approximating the number of distinct elements in a multiset. [1] Calculating the exact cardinality of the distinct elements of a multiset requires an amount of memory proportional to the cardinality, which is impractical for very large data sets. Probabilistic cardinality estimators ...
Then an ordinal number is, by definition, a class consisting of all well-ordered sets of the same order type. To have the same order type is an equivalence relation on the class of well-ordered sets, and the ordinal numbers are the equivalence classes. Two sets of the same order type have the same cardinality.
For example, a machine with states {,,,} has a variety of four states or two bits. The variety of a sequence or multiset is the number of distinct symbols in it. For example, the sequence ,,,,, has a variety of four.
Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections. Include the cardinalities of the triple-wise intersections. Exclude the cardinalities of the quadruple-wise ...
Examples for fuzzy intersection/union pairs with standard negator can be derived from samples provided in the article about t-norms. The fuzzy intersection is not idempotent in general, because the standard t-norm min is the only one which has this property. Indeed, if the arithmetic multiplication is used as the t-norm, the resulting fuzzy ...
Estimate the cardinality of as /, where . The idea is that if n {\displaystyle n} is the number of distinct elements in the multiset M {\displaystyle M} , then B I T M A P [ 0 ] {\displaystyle \mathrm {BITMAP} [0]} is accessed approximately n / 2 {\displaystyle n/2} times, B I T M A P [ 1 ] {\displaystyle \mathrm {BITMAP} [1]} is accessed ...
In psychology, control is a person's ability or perception of their ability to affect themselves, others, their conditions, their environment or some other circumstance. Control over oneself or others can extend to the regulation of emotions , thoughts , actions , impulses , memory , attention or experiences .