Is this really true?
The idea is that 0.9 recurring
(0.999...,
with the digits going on forever)
is actually equal to 1
(For this exercise I will use the notation 0.999...
as notation for 0.9 recurring,
the correct way would be to put a little dot above the 9, or a line on top like this: 0.9)
Does 0.999... = 1 ? |
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Let X = 0.999... |
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Then 10X = 9.999... |
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Subtract X from each side to give us: |
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9X = 9.999... - X |
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but we know that X is 0.999..., so: |
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9X = 9.999... - 0.999... |
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9X = 9 |
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Divide both sides by 9: |
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X = 1 |
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But hang on a moment I thought we said
X was equal to 0.999... ?
Yes, it does, but from our calculations X is also equal to
1. So: |
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X = 0.999... = 1 |
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Therefore 0.999... = 1 |
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