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)
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 


• 
Therefore 0.999... = 1 





