> [!summary] A set is a collection of elements >[!info]+ Read Time **⏱ 1 min** # Definition A set is a collection of objects of vectors. A set has no "rules" on how vectors behave or interact; it's just a list. Formally, a set usually contains vectors from a [[Vector Spaces|vector space]], like $\mathbb{R}^n$ where $ S = \left\{ \vec{v_{1}},\vec{v_{2}}\dots v_{k} \right\}\quad | v_{i} \in \mathbb{R}^n $ > [!note] Note that vectors or elements in a set are well defined, meaning that there is no ambiguity about whether something belongs in a set A set can be finite e.g. $\left\{ v_{1},v_{2} \right\}$ A set can be infinite e.g. $\left\{ \vec{v} \in \mathbb{R}^2 \space | \vec{v}=t \begin{bmatrix} 1\\ 2\end{bmatrix}, \space t \in \mathbb{R}\right\}$. Note this set is infinite because $t$ can be any [[Real Numbers|real number]].