In grammar, "transitive" refers to a type of verb that requires a direct object to complete its meaning. For example, in the sentence "She kicked the ball," the verb "kicked" is transitive because it needs the object "ball" to clarify what was kicked. Without the object, the sentence would feel incomplete. In mathematics, "transitive" describes a relationship where if one element is related to a second, and that second element is related to a third, then the first element is also related to the third. For instance, if A is taller than B, and B is taller than C, then A is taller than C. This property helps in understanding various mathematical concepts and structures.