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These works of G. Cantor and Dedekind were of the greatest importance in the progress of the subject.
Dedekind and Peano have worked out such ordinal theories of the number concept.
It follows from axioms 1-12 by projection that the Dedekind property is true for all lines.
The last axiom of order is that there exists at least one straight line for which the point order possesses the Dedekind property.
An open series is continuous if it is compact and possesses the Dedekind property.