Practice Conclusion (7.5) - Cantor's Theorem - Discrete Mathematics - Vol 2
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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define cardinality.

💡 Hint: Think about how we count items in a group.

Question 2 Easy

What is a power set?

💡 Hint: Recall how subsets can form from the original set.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does Cantor's theorem state about set A and its power set P(A)?

|A| = |P(A)|
|A| < |P(A)|
|A| > |P(A)|

💡 Hint: Reflect on the relationship between a set and its subsets.

Question 2

Is the following statement true or false? 'The power set of a countably infinite set is also countably infinite.'

True
False

💡 Hint: Think about how many subsets can be formed from infinite sets.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Create a set A with 3 elements and list all its subsets. Discuss the cardinality of A and P(A).

💡 Hint: Count both the set and its subsets carefully.

Challenge 2 Hard

Discuss the implications of Cantor's theorem using a real-world analogy or its effects on mathematical theory.

💡 Hint: Reflect on how understanding different infinities affects both math and science.

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