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Is this really true?
The conjecture is that 0.9 recurring (i.e. 0.9999....9) 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)
Let X = 0.999...
Then 10X = 9.999...
Subtract X from each side to give us:
9X = 9.999... - X
but we know that X is 0.999..., so:
9X = 9.999... - 0.999...
or: 9X = 9
Divide both sides by 9:
X = 1
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 one. So:
X = 0.999... = 1
Therefore 0.999... = 1
Does anyone disagree with this? Let me know using the math is fun forum.
No, this is not true, properly following the initial equation set out we find that.
X=.999
10X=9.99
Yet,
9X=8.991, and not in fact 9.999, so following through X=8.991/9 being .999 so X conforms to the expected solution.
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