Editing Subset (section)

== Examples of subsets ==
[[File:PolygonsSet EN.svg|thumb|The [[regular polygon]]s form a subset of the polygons.]]
* The set A = {1, 2} is a proper subset of B = {1, 2, 3}, thus both expressions <math>A \subseteq B</math> and <math>A \subsetneq B</math> are true.
* The set D = {1, 2, 3} is a subset (but {{em|not}} a proper subset) of E = {1, 2, 3}, thus <math>D \subseteq E</math> is true, and <math>D \subsetneq E</math> is not true (false).
* The set {''x'': ''x'' is a [[prime number]] greater than 10} is a proper subset of {''x'': ''x'' is an odd number greater than 10}
* The set of [[natural number]]s is a proper subset of the set of [[rational number]]s; likewise, the set of points in a [[line segment]] is a proper subset of the set of points in a [[:line (mathematics)|line]]. These are two examples in which both the subset and the whole set are infinite, and the subset has the same [[Cardinality#Infinite sets|cardinality]] (the concept that corresponds to size, that is, the number of elements, of a finite set) as the whole; such cases can run counter to one's initial intuition.
* The set of [[Rational number|rational numbers]] is a proper subset of the set of [[real number]]s. In this example, both sets are infinite, but the latter set has a larger cardinality (or {{em|power}}) than the former set.

Another example in an [[Euler diagram]]:

<gallery widths="270">
File:Example of A is a proper subset of B.svg|A is a proper subset of B.
File:Example of C is no proper subset of B.svg|C is a subset but not a proper subset of B.
</gallery>