- Binary set
A

**binary set**is a set with (exactly) two distinct elements, or, equivalently, a set whosecardinality istwo .Examples:

* The set {"a","b"} is binary.

* The set {"a","a"} is not binary, since it is the same set as {"a"}, and is thus a singleton.In

axiomatic set theory , the existence of binary sets is a consequence of theaxiom of empty set and theaxiom of pairing . From the axiom of empty set it is known that the set $emptyset\; =\; \{\}$ exists. From the axiom of pairing it is then known that the set $\{emptyset,emptyset\}\; =\; \{emptyset\}$ exists, and thus the set $\{\{emptyset\},emptyset\}$ exists. This latter set has two elements.**ee also***

ordered pair

*binary relation

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