Would the cardinality of a set S = {a, b, {c, d}} be 5?

In summary, the cardinality of the set S = {a, b, {c, d}} is 3, as the elements are a, b, and {c,d}. However, if we let H = {c,d}, then S = {a, b, H} and there is a possibility for more than 3 elements to be pulled out of S if H ⊂ S.
  • #1
Gear300
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Would the cardinality of a set S = {a, b, {c, d}} be 5?
 
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  • #2


Gear300 said:
Would the cardinality of a set S = {a, b, {c, d}} be 5?

No, 3. The elements of the set are a, b, and {c,d}.
 
  • #3


some_dude said:
No, 3. The elements of the set are a, b, and {c,d}.

But let us say that H = {c,d}. Then S = {a, b, H}. Shouldn't it be so that if H ⊂ S, c ϵ H, and d ϵ H, then c ϵ S and d ϵ S...which would mean that you could pull out more than 3 elements out of S (unless it is improper to associate elements of a particular element of a set to that set).
 
Last edited:
  • #4


H ϵ S, not H ⊂ S
 
  • #5


I see...Thanks for the replies.
 

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

Cardinality refers to the number of elements in a set. It can also be thought of as the size or count of the set.

2. How is cardinality determined in a set?

The cardinality of a set is determined by counting the number of distinct elements in the set. In other words, you count how many different objects are in the set.

3. Does the order of elements in a set affect its cardinality?

No, the cardinality of a set is not affected by the order of its elements. As long as the set contains the same number of distinct elements, the cardinality will remain the same.

4. How does the inclusion of a set within another set affect the cardinality?

The inclusion of a set within another set does not affect the cardinality of the larger set. The cardinality is still determined by the number of distinct elements in the set, regardless of any subsets within it.

5. Can the cardinality of a set ever be a fraction or negative number?

No, the cardinality of a set is always a whole number. It represents the count of distinct elements, which cannot be a fraction or negative number.

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