Does cardinality of a set refer to the number of elements it has?

In summary, the cardinality of a set refers to the number of distinct elements in the set, while the size takes into account duplicates. The cardinality can be infinite if the set contains an infinite number of elements, and it is denoted by |S|, where S is the set. The order of elements does not affect the cardinality of a set.
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yakin
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Is cardnality of a set refers to the number of elements that set has?
 
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  • #2
yakin said:
Is cardnality of a set refers to the number of elements that set has?
It does not only refer to the number of elements; it is that number. :) For infinite sets, though, it is more complicated.
 

Related to Does cardinality of a set refer to the number of elements it has?

1. What is the definition of cardinality of a set?

The cardinality of a set refers to the number of distinct elements contained within the set.

2. How is the cardinality of a set different from its size?

The size of a set refers to the total number of elements, including duplicates, while the cardinality only considers distinct elements.

3. Can the cardinality of a set be infinite?

Yes, the cardinality of a set can be infinite if the set contains an infinite number of elements. For example, the set of all natural numbers has an infinite cardinality.

4. How is the cardinality of a set denoted?

The cardinality of a set is often denoted by the symbol |S|, where S is the set in question. For example, if the set S = {1,2,3}, then |S| = 3.

5. Is the cardinality of a set affected by the order of its elements?

No, the cardinality of a set is not affected by the order of its elements. For example, the sets {1,2,3} and {3,2,1} have the same cardinality of 3.

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