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→The empty set
The empty set is the set with no members. Because sets are uniquely defined by membership, the empty set is unique. The empty set is usually denoted by {} or ∅.
The empty set is the set with no members. Because sets are uniquely defined by membership, the empty set is unique. The empty set is usually denoted by {} or ∅.
In the axiomatic set theory, '''any''' other set is build over the empty set. For example, an example of a set with one element is the set { ∅ } - the set whose single element is the empty set. Von Neumann called the empty set ''0'', and this set { ∅ } = ''1'', and proceeded in defining each ''natural number'' ''n'' as the set with the n elements from 0 to n-1. In this way, it's possible to define the (infinite) set of natural numbers. Ordered pairs, functions, relations, etc, are all defined as sets with some properties.<ref>[https://www.britannica.com/science/set-theory/Schema-for-transfinite-induction-and-ordinal-arithmetic ''Axiomatic set theory''], retrieved from [[Enciclopedia Britannica]] on Apr 15, 2022.</ref><ref>[https://plato.stanford.edu/entries/set-theory/ ''Set Theory''], retrieved from [[Stanford Encyclopedia of Philosophy]] on Apr 15, 2022.</ref>
== See also ==
== See also ==