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 Question from Mac, a student: Hi, Can you please help me to find and verify whether the following are finite, countably infinite and uncountable ? http://www.cs.arizona.edu/~ecarter/473pics/cardinality.pdf 1. countably infinite 2. countably infinite 3. uncountable 4. Can you please tell me what is this notation ? 5. countably infinite (am i correct in this ?) 6. uncountable (am i correct in this ?) 7. finite 8. countably infinite 9. finite 10. countably infinite 11. countably infinite 12. countably infinite 13. can you please explain what it mean ? 14. finite 15. finite 16. no idea 17. countably infinite 18. uncountable And i have few more questions to solve, please help me out to solve that too. 1. {x ∈ R : x2 + 2x − 1 = 0} This one is countably infinite. Because set of all real number's is countably infinite right ? 2. {x ∈ N : x <= 0} This should be finite set. Because natural numbers start from 1. So this is an empty set. 3. {x ∈ Q : 0 <= x <= 1} This should be finite set right ? Thanks Mac

Hi Mac,

I can help with part of this. 1, 2 and 3 are correct. 4 is the complex numbers. 5 is uncountable. 6, 7 and 9 are correct. I don't understand the notation is 8, 10, 11 and 12. 13 is uncountable. 14, 15 and 16 I don't know enough about Turing machines to answer. 17 and 18 are correct.

For your extra questions 2 and 3 are correct. For 1 solve x2 + 2x - 1 = 0. How many solutions do you get?

Harley

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