Let this be the thread discussing the proof of 0.999... = 1
This is their first argument and proof:
(1/9) = (0.1111...)
9(1/9) = 9(0.1111...)
1 = 0.9999...
is similar to this argument
(1/4) = (0.2500...) = (0.2...)
4(1/4) = 4(0.2...)
1 = 0.8...
Which is erroneous.
Second proof: Digit Manipulation
(x) = (0.9999...)
10(x) = 10(0.9999...)
(10x) = 9.999...
(10x)-x = (9.999...) - (0.9999...)
9x = [9] [9 is ERRONEOUS, the answer is 8.9999... look at the argument below]
x = 1
is similar to this argument:
(x) = (0.9999)
10(x) = 10(0.9999)
(10x) = 9.999
(10x)-x = (9.999) - (0.9999)
9x = 8.9991
x = 0.9999
Ok, so since everybody already thinks that 0.9999.. = 1, there's no point trying to add proof that it is. However, is anyone out here brave enough to try prove that 0.9999... != 1
This is their first argument and proof:
(1/9) = (0.1111...)
9(1/9) = 9(0.1111...)
1 = 0.9999...
is similar to this argument
(1/4) = (0.2500...) = (0.2...)
4(1/4) = 4(0.2...)
1 = 0.8...
Which is erroneous.
Second proof: Digit Manipulation
(x) = (0.9999...)
10(x) = 10(0.9999...)
(10x) = 9.999...
(10x)-x = (9.999...) - (0.9999...)
9x = [9] [9 is ERRONEOUS, the answer is 8.9999... look at the argument below]
x = 1
is similar to this argument:
(x) = (0.9999)
10(x) = 10(0.9999)
(10x) = 9.999
(10x)-x = (9.999) - (0.9999)
9x = 8.9991
x = 0.9999
Ok, so since everybody already thinks that 0.9999.. = 1, there's no point trying to add proof that it is. However, is anyone out here brave enough to try prove that 0.9999... != 1