The cardinality of a finite set is the number of elements in the set. The cardinality of infinite sets is infinity but - if you really want to go into it - reflects a measure of the degree of...
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The cardinality of a set is the number of elements in the set.
If set b is finite then the cardinality is the number of elements in it. If it is not finite then it depends on whether its elements can be put into 1-to-1 correspondence with the natural numbers (cardinality = Aleph Null) or with irrationals (Aleph-One).
There are more irrational numbers than rational numbers. The rationals are countably infinite; the irrationals are uncountably infinite. Uncountably infinite means that the set of irrational numbers has a cardinality known as the "cardinality of the continuum," which is strictly greater than the cardinality of the set of natural numbers which is countably infinite. The set of rational numbers has the same cardinality as the set of natural numbers, so there are more irrationals than rationals.
It depends on the set x. If set x is of cardinality n (it has n elements) then it has 2n subsets.
There is no one to one correspondence between the real numbers and the set of integers. In fact, the cardinality of the real numbers is the same as the cardinality of the power set of the set of integers, that is, the set of all subsets of the set of integers.