Null sequence

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I've been dealing with this definition now for over 4 years, trust me, null sequence was quite literally the first thing I learned

Definition

A null sequence is a term for a sequence that converges to $0$.

This term requires a certain amount of structure on the space the sequence is in, namely for a $0$ to make sense, so we're talking on a normed space really. All norms are also metric spaces however metric spaces have no notion of $0$.

Typically first years learn about metrics, and deal with $0\in\mathbb{R}$ this is of course a normed space too.