Eigenschappen

Als $L$ een lineaire ruimte is gelden de volgende

Stellingen

1. $\exists !_{{\bf0} \in L} \forall_{{\bf a} \in L} [ {\bf a} + {\bf0} = {\bf a} ]$
2. $\forall_{{\bf a} \in L} \exists !_{{- \bf a} \in L} [ {\bf a} + (-{\bf a}) = {\bf0} ]$

Definitie ${\bf a} - {\bf b} \equiv {\bf a} + (-{\bf b})$

Stellingen

1. $\forall_{{\bf a},{\bf b},{\bf c} \in L} [ {\bf a} + {\bf b} = {\bf c} \Leftrightarrow {\bf a} = {\bf c} - {\bf b} ]$
2. $\forall_{{\bf a} \in L} [ 0{\bf a} = {\bf0} ]$
3. $\forall_{{\bf a} \in L} [ (-1){\bf a} = -{\bf a} ]$
4. $\forall_{p \in {\mathbb{R}}} [ p{\bf0} = 0 ]$