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What Exactly is an Infinitesimal?

June 7, 2008

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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Benford’s Law

December 10, 2007

Benford’s Law is a fascinating theorem from statistics that states, for most forms of data, the leading digits of numbers are not uniformly distributed among 1 through 9. Instead, any given data point has a 30.1% probability of having a 1 as its leading digit. There is a 17.6% probability of the leading digit being [...]