On 2021-09-04 09:48:40 -0300, Hope Rouselle wrote: > Christian Gollwitzer <aurio...@gmx.de> writes: > > Am 02.09.21 um 15:51 schrieb Hope Rouselle: > >>>>> ls = [7.23, 8.41, 6.15, 2.31, 7.73, 7.77] > >>>>> sum(ls) > >> 39.599999999999994 > >> > >>>>> ls = [8.41, 6.15, 2.31, 7.73, 7.77, 7.23] > >>>>> sum(ls) > >> 39.60000000000001 > >> All I did was to take the first number, 7.23, and move it to the > >> last > >> position in the list. (So we have a violation of the commutativity of > >> addition.) > > > > I believe it is not commutativity, but associativity, that is > > violated.
I agree.
> Shall we take this seriously? (I will disagree, but that doesn't mean I
> am not grateful for your post. Quite the contary.) It in general
> violates associativity too, but the example above couldn't be referring
> to associativity because the second sum above could not be obtained from
> associativity alone. Commutativity is required, applied to five pairs
> of numbers. How can I go from
>
> 7.23 + 8.41 + 6.15 + 2.31 + 7.73 + 7.77
>
> to
>
> 8.41 + 6.15 + 2.31 + 7.73 + 7.77 + 7.23?
Simple:
>>> 7.23 + 8.41 + 6.15 + 2.31 + 7.73 + 7.77
39.599999999999994
>>> 7.23 + (8.41 + 6.15 + 2.31 + 7.73 + 7.77)
39.60000000000001
Due to commutativity, this is the same as
>>> (8.41 + 6.15 + 2.31 + 7.73 + 7.77) + 7.23
39.60000000000001
So commutativity is preserved but associativity is lost. (Of course a
single example doesn't prove that this is always the case, but it can be
seen from the guarantees that IEEE-754 arithmetic gives you that this is
actually the case).
hp
--
_ | Peter J. Holzer | Story must make more sense than reality.
|_|_) | |
| | | h...@hjp.at | -- Charles Stross, "Creative writing
__/ | http://www.hjp.at/ | challenge!"
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