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 Countable sets (Posted on 2016-03-15)
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 No Rating

 Subject Author Date re(3): Interesting Brian Smith 2016-03-16 12:04:02 re(2): Interesting broll 2016-03-16 10:58:52 re: Interesting Brian Smith 2016-03-16 10:17:19 Interesting broll 2016-03-16 08:51:25 Part 4, the reals JayDeeKay 2016-03-15 13:14:16 Sets of all Rationals (Parts 2 and 3) Brian Smith 2016-03-15 12:10:44 part 2 & 3 Daniel 2016-03-15 11:44:42 Set of all Integers (Part 1 Solution) Brian Smith 2016-03-15 10:45:23

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