Bryan Burgers wrote:
>>> 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?
People are confusing equality and inequality -
the nontrivial thing here is to find the smallest positive x
that satisfies the equation 1 + x == x.
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.
And you've changed the subject - the stuff above was talking about
x + 1 /= x, you're demonstrating solutions to a different problem,
finding the smallest
x such that 1 + x == 1. That's the number often called epsilon.
1 + 2.2e-16 /= 1
True
1 + 2.2e-17 /= 1
False
Let's stop confusing ourselves about this.
Brandon
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