When stimulus A = stimulus B and B = stimulus C, if an organism responds to stimulus A as equal to stimulus C, it is said to show transitivity. For example, if the written numbers one, two, three are equivalent to the arithmetic numbers 1, 2, and 3, and these arithmetic numbers are equivalent to sets IX), IX.X), and IX,X,X), it logically follows that one, two, and three are equivalent to sets IX), IX,XI, and IX,X,XI and the relationship is transitive.