Let
x = 0.9999..... (1)
Multiply both sides by 10
10x = 9.9999.... (2)
Subtract (1) from (2)
LHS: 10x - x = 9x
RHS: 9.9999... - 0.9999.... = 9
as LHS=RHS, 9x = 9
so x = 1
but as per (1) x = 0.9999....
So 1 = 0.9999.....
[No trick. This is actually important].
x = 0.9999..... (1)
Multiply both sides by 10
10x = 9.9999.... (2)
Subtract (1) from (2)
LHS: 10x - x = 9x
RHS: 9.9999... - 0.9999.... = 9
as LHS=RHS, 9x = 9
so x = 1
but as per (1) x = 0.9999....
So 1 = 0.9999.....
[No trick. This is actually important].
1 comment:
1/9 = 0.9999...
9*1/9 = 9*0.9999...
1 = 0.9999
End of day.... We are f**ked up!
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