Editing Cardinality (section)

=== Notation and terminology ===
The cardinality, or ''cardinal number'', of a set <math>A</math> is generally denoted by <math>|A|,</math> with a [[vertical bar]] on each side.<ref>{{Cite web |title=Cardinality {{!}} Brilliant Math & Science Wiki |url=https://brilliant.org/wiki/cardinality/ |access-date=2020-08-23 |website=brilliant.org |language=en-us}}</ref> (This is the same notation as for [[absolute value]]; the meaning depends on context.) The notation <math>|A| = |B|</math> means that the two sets {{tmath|A}} and {{tmath|B}} have the same cardinality. The cardinal number of a set <math>A</math> may also be denoted by <math>n(A),</math> <span style="border-top: 3px double;"><math>A</math></span>, <math>\operatorname{card}(A),</math> <math>\#A,</math> etc.
It is conventional to recognize three kinds of cardinality:
*Any set ''X'' with cardinality less than that of the [[natural number]]s, or | ''X'' | < | '''N''' |, is said to be a [[finite set]].
*Any set ''X'' that has the same cardinality as the set of the natural numbers, or | ''X'' | = | '''N''' | = <math>\aleph_0,</math> is said to be a [[countably infinite]] set.<ref name=":1" />
*Any set ''X'' with cardinality greater than that of the natural numbers, or | ''X'' | > | '''N''' |, for example | '''R''' | = <math>\mathfrak c </math> > | '''N''' |, is said to be [[uncountable set|uncountable]].