Question about cadinality of sets

Thread starter camboguy
Start date May 2, 2010
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Sets

In summary, the cardinality of a set refers to the number of elements in that set. It can be determined by counting the distinct elements or using mathematical operations. Two sets can have the same cardinality and it can be used in other mathematical concepts to determine the number of possible outcomes or elements. The difference between finite and infinite cardinality is that finite sets have a countable number of elements while infinite sets have an uncountable number.

May 2, 2010

camboguy

i was confused about what the cardinality of the set {1,2,2,3,3,1,1,1} is?
is it 8 or is it 3?

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May 2, 2010

pbandjay

Every element of a set is unique, therefore {1,2,2,3,3,1,1,1} is the same as {1,2,3}.

May 3, 2010

g_edgar

There is an alternate concept of "multi-set" if you want to take repeats into account.

1. What is the cardinality of a set?

The cardinality of a set is the number of elements or objects in that set. It is also known as the size or number of elements in a set.

2. How is the cardinality of a set determined?

The cardinality of a set is determined by counting the number of distinct elements in the set. This can be done by listing out the elements or using mathematical operations such as union, intersection, and complement.

3. Can two sets have the same cardinality?

Yes, two sets can have the same cardinality if they contain the same number of elements. For example, the sets {1, 2, 3} and {a, b, c} both have a cardinality of 3.

4. What is the difference between finite and infinite cardinality?

Finite cardinality refers to sets that have a specific, countable number of elements. Infinite cardinality refers to sets that have an uncountable number of elements, such as the set of real numbers.

5. How does the concept of cardinality apply to other mathematical concepts?

The concept of cardinality is often used in other mathematical concepts such as functions, relations, and sequences. It helps to determine the number of possible outcomes or elements in these concepts.