Is this really true?
The conjecture is that 0.9 recurring
(i.e. 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)
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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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or: •
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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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