Tail of a sequence ($(x_n{)}_{n\ge N}$)

A tail of a sequence consists of its terms from some index $N$ onward, retaining their order and repetitions. Discarding finitely many initial terms does not change its limit of a sequence or whether it is a Cauchy sequence. A tail can also be considered as the set of values $\{x_n:n\ge N\}$ when forming an infimum, supremum, or tail diameter of a sequence; that set alone forgets the original order and repetitions.