x_{1} is an eventual/tail(-end) x_{2} of x_{3}; x_{3} eventually is/has/is characterized by x_{2}(/-ic/ness)

When x_{3 (n)} is understood as a sequence in one variable n (which is well-understood in the definition thereof), then there exists some real number N such that for any n > N, x_{2} holds true for x_{1} when considering such x_{3 (n)}; in other words, x_{1} is an x_{2} for the tail of x_{3}. Examples: "eventually periodic", "eventually bounded", etc.