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Cardinality is a measure of the size of a [[set theory|set]]. For [[finite]] sets, its cardinality is simply the number of elements in it.
'''Cardinality''' is a measure of the size of a [[set theory|set]]. For [[finite]] sets, its cardinality is simply the number of elements in it.
For example, there are 7 days in the week (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday), so the cardinality of the set of days of the week is 7. Similarly, there are 26 letters in the [[alphabet]], so the set of letters of the alphabet has cardinality 26. As another example, the set of suits for [[playing card]]s is 4 (there are four suits, hearts, diamonds, clubs and spades).
For example, there are 7 days in the week (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday), so the cardinality of the set of days of the week is 7. Similarly, there are 26 letters in the [[alphabet]], so the set of letters of the alphabet has cardinality 26. As another example, the set of suits for [[playing card]]s is 4 (there are four suits, hearts, diamonds, clubs and spades).
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]]