Affine Group of One Dimension is Group/Proof 2
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Theorem
Let $\map {\operatorname {Af}_1} \R$ be the $1$-dimensional affine group on $\R$.
Then $\map {\operatorname {Af}_1} \R$ is a group.
Proof
It follows from Affine Group of One Dimension as Semidirect Product and Semidirect Product of Groups is Group.
$\blacksquare$