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Cardinality is simply the number of elements of a given set. You can use the cardinality of a set to determine which elements will go into the subset. Every element in the subset must come from the cardinality of the original set. For example, a set may contain {a,b,c,d} which makes the cardinality 4. You can choose any of those elements to form a subset. Examples of subsets may be {a,c} {a, b, c} etc.

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Q: How cardinality relates to the number of subsets of a set?

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No. The number of subsets of that set is strictly greater than the cardinality of that set, by Cantor's theorem. Moreover, it's consistent with ZFC that there are two sets which have different cardinality, yet have the same number of subsets.

A fraction is a number, it is not a set. A number cannot have subsets, only a set can.

The cardinality of 15 is equal to the number of elements in the set. Since 15 is only one number, its cardinality is 1.

The number of elements. A set with n elements has 2n subsets; for example, a set with 5 elements has 25 = 32 subsets.

The cardinality of a finite set is the number of distinct elements in the set. For infinite sets, the cardinality is Aleph-Null if the elements of the set can be put into 1-to-1 relationship with the natural numbers: that is, if the set is countably infinite. However, the set of irrational numbers, for example, has a number of elements which is a greater order of infinity (uncountably infinite). It's cardinality is denoted by C, for "continuum".

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Assuming no restrictions on the set, the cardinality of a set, n, is related in this form # of subsets = 2n

If a set has "n" elements, then it will have 2n subsets. This number of subsets is always larger than the number of elements - whether the set is finite or infinite.

No. The number of subsets of that set is strictly greater than the cardinality of that set, by Cantor's theorem. Moreover, it's consistent with ZFC that there are two sets which have different cardinality, yet have the same number of subsets.

It is impossible. If a set has n elements, the cardinality of its power set [the number of its subsets] is 2n which must be even.

It depends on the set x. If set x is of cardinality n (it has n elements) then it has 2n subsets.

The cardinality of a set is the number of elements in the set.

even though its carnality is 0 one of its properties says that the only subset of the null set is the empty set * * * * * Carnality refers to sexual desires and I would be greatly surprised if the null set had any of those! The number of subsets of a set whose cardinality is C(S) is 2C(S). The cardinality of the null set is, as the answer was trying to say, 0. So the number of its subsets is 2C(S) = 20 = 1. A null set has one subset - which is also a null set.

A fraction is a number, it is not a set. A number cannot have subsets, only a set can.

00 is not a set but the number zero written as a 2-digit number. The set {00} has cardinality 1.

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...

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...

The cardinality of 15 is equal to the number of elements in the set. Since 15 is only one number, its cardinality is 1.

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