What Exactly is an Infinitesimal?

What Exactly is an Infinitesimal?

During the 1800s, mathematicians, and especially Cauchy, finally got around to rigorizing calculus. They got rid of the “infinitesimal” business once and for all, replacing infinitesimals with limits. It is troubling how widespread misunderstanding of calculus is 150 years later. Instead of understanding calculus from Cauchy’s rigorous standpoint, people embrace a hodge-podge of infinitesimals AND limits.

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