A Cantorian Argument against Infinitesimals

In 1887 Georg Cantor gave an influential but cryptic proof of the impossibility of infinitesimals. I first give a reconstruction of Cantor's argument which relies mainly on traditional assumptions from Euclidean geometry, together with elementary results of Cantor's own set theory. I then apply the reconstructed argument to the infinitesimals of Abraham Robinson's nonstandard analysis. This brings out the importance for the argument of an assumption I call the Chain Thesis. Doubts about the Chain Thesis are seen to render the reconstructed argument inconclusive as an attack on the infinitely small.