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Similarly, the multiples of 3 (3, 6, 9, 12, 15...), 4 (4, 8, 12, 16, 20, 24, 28... and so on, each form a countable set, as each can be written as a list.

Similarly, the multiples of 3 (3, 6, 9, 12, 15...), 4 (4, 8, 12, 16, 20, 24, 28... and so on, each form a countable set, as each can be written as a list.

One unusual property of infinite sets is that a "smaller" set can have the same cardinality as a "larger" one. For example here we see that the set of even numbers has the same cardinality as the set of natural numbers, and thus it is in a sense the same size, even though the set of even numbers misses out a lot of numbers from the set of natural numbers.

One unusual property of infinite sets is that a "smaller" set can have the same cardinality as a "larger" one. For example, here we see that the set of even numbers has the same cardinality as the set of natural numbers, and thus it is in a sense the same size, even though the set of even numbers misses out a lot of numbers from the set of natural numbers.

[[category: set theory]]

Infinite sets are assigned different cardinalities using the Hebrew symbol <math>\aleph</math> ([[aleph]]), for example the natural numbers have cardinality <math>\aleph_0</math>.

 

[[Category:Set Theory]]