Editing Unit interval (section)

===Cardinality===
{{Main|Cardinality of the continuum}}

The ''size'' or ''[[cardinality]]'' of a set is the number of elements it contains.

The unit interval is a [[subset]] of the [[real number]]s <math>\mathbb{R}</math>. However, it has the same size as the whole set: the [[cardinality of the continuum]]. Since the real numbers can be used to represent points along an [[Real line|infinitely long line]], this implies that a [[line segment]] of length 1, which is a part of that line, has the same number of points as the whole line. Moreover, it has the same number of points as a square of [[area]] 1, as a [[cube]] of [[volume]] 1, and even as an unbounded ''n''-dimensional [[Euclidean space]] <math>\mathbb{R}^n</math> (see [[Space filling curve]]).

The number of elements (either real numbers or points) in all the above-mentioned sets is [[Uncountable set|uncountable]], as it is strictly greater than the number of [[natural number]]s.