Exploring the Meaning of ##n(A)##

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In summary, ##n(A)## represents the cardinality or number of elements in a set A, and it can be calculated by counting the distinct elements in the set. The cardinality of a set can be infinite, and it is different from the cardinal number, which represents the numerical value of the cardinality. Cardinality is an important concept in mathematics that is used in various areas such as set theory, combinatorics, and probability to determine the number of possible outcomes.
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attachment.php?attachmentid=70965&stc=1&d=1404035528.png

##n(A)##
I have some doubts.
Obviously, ##n(A)## means the number of elements in set A.
Should it be 3 or 6?

Should I consider each number to be a different element?
 

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The names of the elements are irrelevant. If you change the names ##\{1,2,3\}## by ##\{a,b,c\}##, then it will have the same number of elements. Does that answer your question?
 
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micromass said:
The names of the elements are irrelevant. If you change the names ##\{1,2,3\}## by ##\{a,b,c\}##, then it will have the same number of elements. Does that answer your question?
Yes, thank you :smile:
 

1. What does ##n(A)## represent?

##n(A)## represents the cardinality or the number of elements in set A. It is a way to measure the size or quantity of a set.

2. How is ##n(A)## calculated?

The cardinality of a set can be calculated by counting the number of distinct elements in the set. For example, if set A = {1, 2, 3, 4}, then ##n(A)## = 4.

3. Can the cardinality of a set be infinite?

Yes, the cardinality of a set can be infinite. For example, the set of all positive integers has an infinite cardinality.

4. What is the difference between cardinality and cardinal number?

Cardinality refers to the size or quantity of a set, while cardinal number refers to the numerical value that represents the cardinality. For example, if a set has a cardinality of 5, the cardinal number would be 5.

5. How is cardinality used in mathematics?

Cardinality is used in various mathematical concepts such as set theory, combinatorics, and probability. It is an important tool for determining the number of possible outcomes in a given scenario.

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