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Not looking for a solution necessarily, but just trying to understand why this issue occurrs.

I have a 'Do' loop which iterates some algorithm over values of a parameter 'x' with range {x,0,1,0.1} and creates a list of lists, called "AllData", with results of the algorithm and Prepends the value of x to the results of each iteration. So AllData looks something like this: {{0., results},{0.1, results}, ..., {1.`, results}} where the first position gives the value of x.

But, 'AllData' has floating-point errors for some values of 'x' (not all). So - instead of of x=0.3, it has x=0.30000000000000004 instead of of x=0.6, it has x=0.60000000000000001 instead of of x=0.7, it has x=0.70000000000000001

This is fine, except, when I want to separate AllData using Select, only some of the errors are recognized as such. I run Do[SpecificData[y]=Select[AllData, #[[1]]==y &],{y,0,1,0.1}]

The code mostly works. All SpecificData[y] (including SpecificData[0.3] and SpecificData[0.6]) are created just fine. But SpecificData[0.7] fails to recognize the elements where the value of 'x' is 0.70000000000000001`. OR perhaps it uses slightly different value of 0.7. Either way, if I try to output SpecificData[0.7], it gives no output. BUT, if I output "SpecificData[0.3]" or "SpecificData[0.6]", it gives an output.

If I manually change 0.70000000000000001`to 0.7 in AllData, and try to use the Select loop, it still fails to create SpecificData[0.7], which to me suggests that even the second Do loop (where I create SpecificData) is using slightly different value of 0.7.

I'm trying to understand why 0.30000000000000004 and 0.60000000000000001 are recognized as 0.3 and 0.6, but 0.70000000000000001` is not recognized as 0.7. Also, why is the simple Do loop adding floating-point error in some numbers and not in others?

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    $\begingroup$ The moral lesson is that you should have done {x, 0, 1, 1/10} instead. See this older thread. $\endgroup$
    – J. M.'s lack of A.I. ♦
    Jun 10, 2022 at 15:57
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    $\begingroup$ True. That's what I am doing now. But I still am curious for why this happens. $\endgroup$
    – Ssdmitten
    Jun 10, 2022 at 16:02
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    $\begingroup$ It's because floating points are dyadic, whereas 0.1 is not. The floating point value of 0.1 is 0.10000000000000000555. Sometimes this will make Do accidentally fail to reach the end value. I often use something like {x, N[Subdivide[0, 1, 10]]} to prevent that $\endgroup$
    – Coolwater
    Jun 10, 2022 at 16:56
  • $\begingroup$ Ah! This made me do a dive into floating point calculation, and I see the problem. Thanks for the solutions and for prompting me to learn something new. $\endgroup$
    – Ssdmitten
    Jun 23, 2022 at 20:28

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