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moo5003
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Is it true that the set of permutations on a infinite set K has the same cardinality as all functions between a infinite set K to itself?
The cardinality of a function is the number of elements in the function's domain. It represents the size or amount of inputs that the function can take.
The cardinality of a function is determined by counting the number of elements in the function's domain. This can be done by listing out all the inputs or using mathematical notation to represent the size of the domain.
Yes, the cardinality of a function can be infinite. This means that the function has an uncountable number of elements in its domain, such as in the case of real numbers or continuous functions.
The cardinality of a function can affect its properties in terms of its injectivity, surjectivity, and bijectivity. For example, a function with a smaller cardinality in its domain may have more restrictions and limitations compared to a function with a larger cardinality in its domain.
Yes, there can be a relationship between the cardinality of a function and its range. For example, in some cases, a function may have the same cardinality in its domain and range, while in other cases, the cardinality of the range may be smaller than the cardinality of the domain.