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Countable sets (Posted on 2016-03-15) Difficulty: 3 of 5
A set is countable if and only if each of its elements can be associated with a different positive integer. Every finite set is countable. For example, the set {2, 3, 5, 7, 11} is countable.

1↔2
2↔3
3↔5
4↔7
5↔11

Infinite sets can also be countable. For example, the set of all prime numbers is countable.

1↔2
2↔3
3↔5
4↔7
5↔11
6↔13
7↔17
8↔19
9↔23
10↔29
...

1. Is the set of all integers countable?
2. Is the set of all positive rational numbers countable?
3. Is the set of all rational numbers countable?
4. Is the set of all positive real numbers countable?
5. Is the set of all real numbers countable?

No Solution Yet Submitted by Math Man    
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  Subject Author Date
re(3): InterestingBrian Smith2016-03-16 12:04:02
re(2): Interestingbroll2016-03-16 10:58:52
re: InterestingBrian Smith2016-03-16 10:17:19
Interestingbroll2016-03-16 08:51:25
Part 4, the realsJayDeeKay2016-03-15 13:14:16
Some ThoughtsSets of all Rationals (Parts 2 and 3)Brian Smith2016-03-15 12:10:44
part 2 & 3Daniel2016-03-15 11:44:42
Some ThoughtsSet of all Integers (Part 1 Solution)Brian Smith2016-03-15 10:45:23
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