Atlas Trail
Nothing, Everything and the Instant Between
Five concepts that took mathematics centuries to make rigorous: a number for nothing, an idea for without end, and the machinery, limit, derivative and integral, built on top of both to describe instantaneous change and continuous accumulation.
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Concepts
Treating zero as a genuine number, not just a placeholder, took mathematics centuries longer than the placeholder symbol itself.
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Concepts
The opposite extreme: a quantity or process with no final limit, debated by philosophers for two millennia before mathematics gave it rigorous, working content.
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Concepts
The tool that tames infinity for practical use: a sequence or function approaching a fixed value as closely as desired without necessarily reaching it.
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Concepts
Built directly on the limit: the instantaneous rate of change, independently developed by Newton and Leibniz in the same generation.
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Concepts
The derivative run in reverse: continuous accumulation, joined to the derivative by the fundamental theorem of calculus that Newton and Leibniz each reached on their own.
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