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Re: how to explain this weird effect? Integrate


drbob at bigfoot.com (Bobby R. Treat) wrote concerning the bug which causes
Limit[Floor[Cos[x]], x -> 0] to give 1, rather than 0:

> The problem with Floor[Cos[x]] may be related to this situation:
>
> Floor[1 - 10.^(-17)]
> 1

Thanks. Yes, it might be related to that. But it _shouldn't_ be related
since everything in Limit[Floor[Cos[x]], x -> 0] is _exact_.

BTW, I doesn't trouble me -- well, at least, not much -- that
Floor[1 - 10.^(-17)] yields 1 . I've often mentioned (although perhaps not
in this newsgroup) that using discontinuous functions such as Floor in
floating-point arithmetic is _inherently_ perilous. One needs to learn to
expect things like Floor[1 - 10.^(-17)] possibly being 1 .

OTOH, note that Mathematica correctly gives 0 for Floor[1 - 10^(-17)] .
Since everything there was exact, I would have been greatly troubled if
Mathematica hadn't gotten that right.

David


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