Is this really true?
The idea is that 0.9 recurring
(0.999..., with the digits going on forever)
is actually equal to 1
(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 ? 

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 1. So: 

X = 0.999... = 1 



So 0.999... = 1 



Does anyone disagree with this? Let me
know on the Math is Fun Forum. 

