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3 cards from this section. Quick, good the night before a test.
Define cardinality.
Think about how we count items in a group.
What is a power set?
Recall how subsets can form from the original set.
What does Cantor's theorem state about set A and its power set P(A)?
Reflect on the relationship between a set and its subsets.
Is the following statement true or false? 'The power set of a countably infinite set is also countably infinite.'
Think about how many subsets can be formed from infinite sets.
Create a set A with 3 elements and list all its subsets. Discuss the cardinality of A and P(A).
Count both the set and its subsets carefully.
Discuss the implications of Cantor's theorem using a real-world analogy or its effects on mathematical theory.
Reflect on how understanding different infinities affects both math and science.
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