QUOTE : 4.13. The most striking aspect of Dedekind's definition is that it determines infinity positively, and subordinates the finite negatively. This is its especially modern accent, such as is almost always found in Dedekind. An infinite system has a property of an existential nature: there exists a biunivocal correspondence between it and one of its proper parts. The finite is that for which such a property does not obtain. The finite is simply that which is not infinite, and all the positive simplicity of thought hinges on the infinite.