Definition:Group Axioms/Left

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A group is an algebraic structure $\struct {G, \circ}$ which satisfies the following four conditions:

\((\text G 0)\)   $:$   Closure Axiom      \(\displaystyle \forall a, b \in G:\) \(\displaystyle a \circ b \in G \)             
\((\text G 1)\)   $:$   Associativity Axiom      \(\displaystyle \forall a, b, c \in G:\) \(\displaystyle a \circ \paren {b \circ c} = \paren {a \circ b} \circ c \)             
\((\text G_{\text L} 2)\)   $:$   Left Identity Axiom      \(\displaystyle \exists e \in G: \forall a \in G:\) \(\displaystyle e \circ a = a \)             
\((\text G_{\text L} 3)\)   $:$   Left Inverse Axiom      \(\displaystyle \forall a \in G: \exists b \in G:\) \(\displaystyle b \circ a = e \)             

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