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In everyday language, infinity and limits sound like they contradict each other, but in calculus they are welded together as part of a single, overarching concept. In fact it is probably the most revolutionary concept in all of calculus, the one that distinguishes this branch of math from all that came before—algebra, geometry, and trigonometry.

The great achievement of calculus is the domestication of infinity. The concept of infinity itself had long been avoided and even feared. The Greeks thought it made no sense. During the Renaissance, the Church forbade anyone to write about infinity—and Giordano Bruno was burned at the stake for violating that edict—because only God...


Cover of The Calculus of Friendship


The concept of infinity