 Torsion-free abelian group axiom scheme (source code)

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= Torsion-free abelian group axiom scheme
{title2=$\forall x(nx=0\to x=0),\quad n\ge1$}

For an <abelian group>, the scheme $\forall x(nx=0\to x=0)$ for every positive integer $n$ expresses absence of nonzero elements of <finite order>. Each fixed $n$ gives one sentence, while the entire scheme expresses the <torsion-free abelian group> property.

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