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by techno_tsar
670 days ago
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There's a rigorous proof on Wikipedia, but there's simpler ways to show it. For example, we know that 1/3 = 0.333... 3 * 1/3 = 3 * 0.333... 1 = 0.999... You can also do it with subtraction. For example, 1 - 0.999... = x. Assuming x is greater than 0, then it should evaluate to 0.000...1. But we can't have the digit 1 after an infinite number of zeros. If there truly were a "1" after infinite zeros, it implies reaching the end of infinity, which is a logical contradiction. So x can't be greater than 0. |
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