---- > [!definition] Definition. ([[affine space]]) > The model affine space: For $K$ a field, $\mathbb{A}^{n}_{k}$ denotes the [[affine space]] of dimension $n$ over $K$, that is, the set of $k$-tuples of elements in $K$:$\mathbb{A}^{n}_{K}=\{ (c_{1},\dots,c_{n}): c_{i} \in k \}.$ Elements of $\mathbb{A}^{n}_{K}$ are called **points**. As a set, $\mathbb{A}^{n}_{K}$ is the same as $K^{n}$; however, the latter notation is reserved to denote a [[vector space]] — extraneous structure for which $\mathbb{A}^{n}_{K}$ has no use. ^definition ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```