= Weakly linear partial function
{title2=$f(x+y)=f(x)+f(y),\qquad q\operatorname{dom}(f)\subseteq\operatorname{dom}(f)\ (q\in\mathbb Q)$}
= Weakly linear function
{synonym}
A <weakly linear partial function> on the <real numbers> has a domain closed under rational <scalar multiplication> and <addition>, and it preserves <addition> on that domain. A nonempty domain is a <vector space over the rational numbers>, and additivity implies <rational homogeneity of an additive function> by <integer> <multiplication> and division. The <empty function> also satisfies the defining conditions vacuously. This terminology does not assert homogeneity under arbitrary real scalars.
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