Tail of a sequence (source code)

= Tail of a sequence
{title2=$(x_n)_{n\geq N}$}

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 $\{x_n:n\geq N\}$ when forming an <infimum>, <supremum>, or <tail diameter of a sequence>; that <set> alone forgets the original order and repetitions.