1 = 0.999999....
This is what i discovered 5 years ago.
let x = 0.9999...
(1) x = 0.9999... - given
(2) 10x = 9.9999... - multiply both sides of (1) by 10
(3) 9x = 9 - subtract (1) from (2)
(4) x = 1 - divide both sides of (3) by 9
(5) 1 = 0.9999... - substitute x with (1)
To all mathematics enthusiast, hope you have read this and share this with others.
let x = 0.9999...
(1) x = 0.9999... - given
(2) 10x = 9.9999... - multiply both sides of (1) by 10
(3) 9x = 9 - subtract (1) from (2)
(4) x = 1 - divide both sides of (3) by 9
(5) 1 = 0.9999... - substitute x with (1)
To all mathematics enthusiast, hope you have read this and share this with others.
posted by Ozting at 10:12 PM
2 Comments:
Um... no. 10x-1 has to stay as is. You can't subtract a number from a variable without replacing the variable first.
What happens in step 3 is that
10x - x = 9.9999... - 0.9999...
9x = 9
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