Homework Sourse1 Determine whether each of these sets is finite countably i
1. Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.
\"This is not multiple questions, is all one question\"
a) The integers greater than 10
The set is countably infinite.
The set is finite.
The set is countably infinite with one-to-one correspondence 1 ? 11, 2 ? 12, 3 ? 13, and so on.
The one-to-one correspondence is given by n ? (n + 10).
The set is countably infinite with one-to-one correspondence 1 ? 10, 2 ? 12, 3 ? 17, and so on.
The one-to-one correspondence is given by n ? (2n + 10).
b) The odd negative integers
The set is countably infinite.
The set is finite.
The set is countably infinite with one-to-one correspondence 1 ?
| The set is countably infinite. | |
| The set is finite. | |
| The set is countably infinite with one-to-one correspondence 1 ? 11, 2 ? 12, 3 ? 13, and so on. | |
| The one-to-one correspondence is given by n ? (n + 10). | |
| The set is countably infinite with one-to-one correspondence 1 ? 10, 2 ? 12, 3 ? 17, and so on. | |
| The one-to-one correspondence is given by n ? (2n + 10). |
Solution
A.
The set is countably infinite with one-to-one correspondence 1 ? 11, 2 ? 12, 3 ? 13, and so on.
B.
The set is countably infinite with one-to-one correspondence 1 ?
