How to Express Sets with Specific Cardinality Restrictions?

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In the expression of sets: B={X \in A:|X|<3} the expression is saying that B is a set that contains at most 3 sets X that belongs to A, right?

How do we say, B is a set that contains elements of X that belongs to A, and all X elements contains at most 3 x elements (the cardinality of X is at most 2). For example, B={{1,2},{3}}. And not, B={{1,2,3}}
 
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hi xeon123! :smile:
xeon123 said:
In the expression of sets: B={X \in A:|X|<3} the expression is saying that B is a set that contains at most 3 sets X that belongs to A, right?

no, it's saying that B is the collection of all elements of A with less than 3 elements
 
xeon123 said:
How do we say, B is a set that contains elements of X that belongs to A, and all X elements contains at most 3 x elements (the cardinality of X is at most 2). For example, B={{1,2},{3}}. And not, B={{1,2,3}}
Assuming you meant "B is the set that consists of elements X that belong to A and which contain at most 2 elements" then: B={X \in A:|X|<3}
Your example works provided that the only elements of A with less than three elements are the two you show.
 
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