Let $(a_n)_{n\in \mathbb N}$ be the sequence of points in a set $X$. The subset $M\subset X$ with $M:=\{a_n\in X:~n\in\mathbb N\}$ is called the carrier set (or the underlying set) of the sequence $(a_n)_{n\in \mathbb N}$.
Definitions: 1 2
Lemmas: 3 4
Proofs: 5 6
