11. :is an associative binary operation . 12. The binary operations of set identities. 13. The notion of binary operation is meaningless without the set on which the operation is defined. 14. Groups just have one binary operation . 15. This property is shared by most binary operations , but not subtraction or division or octonion multiplication. 16. The works of composition of continuous functions of a single variable and the binary operation of addition. 17. The properties below include a defined binary operation , relative complement, denoted by infix " \ ". 18. They comprise a set and a closed binary operation , but do not necessarily satisfy the other conditions. 19. To the extent possible the defining properties are formulated in terms of the binary operations in the semigroups. 20. Biquandles and biracks have two binary operations on a set X written a ^ b and a _ b.