Hang on, hang on, now I'm getting confused. First you asked for the smallest (positive) x such that 1+x /= x which is around x=4.5e15.
1 + 0 /= 0
0 is smaller than 4.5e15
So I don't understand this at all...
But then 0 isn't positive.
Why not? In any case every positive number nust satisfy the above inequation so what about 0.1, which is certainly smaller than 4500000000000000?
In math, every positive number must satisfy the above inequation, that is true. But as Chad said, the smallest number in Haskell (at least according to my GHC, it could be different with different processors, right?) that satisfies the equation is 2.2e-16.
1 + 2.2e-16 /= 1 True 1 + 2.2e-17 /= 1 False
This is because the Double type only holds so much precision. After getting small enough, the type just can't hold any more precision, and the value is essentially 0.
last $ takeWhile (\x -> 1 + x /= 1) (iterate (/2) 1) 2.220446049250313e-16