More on the cardinality of sets

HOME

Math Central

Quandaries & Queries

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

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.