Algebraic Proofs
Algebraic proofs showing that 0.999... represents the number 1 use concepts such as fractions, long division, and digit manipulation to build transformations preserving equality from 0.999... to 1.
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“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
—Henry David Thoreau (1817–1862)
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—David Hume (1711–1776)