The cardinality of finite sets are the number of elements included in them however, union of infinite sets can be different as it includes the matching of two different sets one by one and finding a solution by matching the same amount of elements in those sets.
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Two sets are equivalent if they have the same cardinality. For finite sets this means that they must have the same number of distinct elements. For infinite sets, equal cardinality means that there must be a one-to-one mapping from one set to the other. This can lead to some counter-intuitive results. For example, the cardinality of the set of integers is the same as the cardinality of the set of even integers although the second set is a proper subset of the first. The relevant mapping is x -> 2x.
The union of two sets.The union of two sets.The union of two sets.The union of two sets.
Infinity squared is infinity. But there's more to it.Mathematicians describe different kinds of infinities:The cardinality(number) of natural numbers is called Aleph0 () . This is infinite, and it has some peculiar properties:The cardinality of even numbers is also Aleph0.As is the cardinality of odd numbers.As is the cardinality of rational numbers (which you could view as infinity squared, but it still gives you infinity.The cardinality of countable ordinal numbers is called Aleph1 ().The cardinality of the real numbers is two to the exponent of Aleph0 ( ). The continuum hypothesis says this is equal to Aleph1.Basically, if you square an infinite set from a given cardinality, the cardinality stays the same (meaning Aleph0 squared is still Aleph0, etc.)If your mind just burst(cause mine did! 0_o), do not worry. This is a common reaction to set theory.See the related link for more on Aleph numbers, which are how mathematicians view infinity.
the union of two sets A and b is the set of elements which are in s in B,or in both A and B
The union of two sets A and B is a set that consists of all elements which are either in A, or in B or in both.