The language of set theory is based on a single fundamental relation, called membership. We say that <math>x</math> is a member of <math>A</math> (in symbols <math>x \in A</math>), or that the set <math>A</math> contains <math>x</math> as an element.<ref>The mathematician Giuseppe Peano created the symbol ∈ in 1889 to mean "is an element of," from the Greek epsilon that is the first letter of εἰμί, which means "I am."</ref> The understanding is that a set is determined by its elements; in other words, two sets are deemed equal if they have exactly the same elements,<ref>http://plato.stanford.edu/entries/set-theory/</ref> or, equivalently, if each is a [[subset]] of the other. | The language of set theory is based on a single fundamental relation, called membership. We say that <math>x</math> is a member of <math>A</math> (in symbols <math>x \in A</math>), or that the set <math>A</math> contains <math>x</math> as an element.<ref>The mathematician Giuseppe Peano created the symbol ∈ in 1889 to mean "is an element of," from the Greek epsilon that is the first letter of εἰμί, which means "I am."</ref> The understanding is that a set is determined by its elements; in other words, two sets are deemed equal if they have exactly the same elements,<ref>http://plato.stanford.edu/entries/set-theory/</ref> or, equivalently, if each is a [[subset]] of the other. |