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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.
Infinite sets are assigned different cardinalities using the hebrew symbol <math>\aleph</math>, for example the natural numbers have cardinality <math>\aleph_0</math>.
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]]
[[category: set theory]]