Re: Bruijn babbles bull***

Horand.Gassmann@xxxxxxxxxxxxxx wrote:

On Feb 5, 9:25 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Horand.Gassm...@xxxxxxxxxxxxxx wrote:

Do you accept the infinite expansion 0.3333... as an equivalent to the
ratio 1/3?

Yes. (Because the infinite expansion can be understood as a limit)

Very good. We are making progress. Any countably infinite process that
produces a well-defined limit is pukkah. Would you agree that the
error of this infinite expansion is 0?

No. But due to the definition of a limit, the error is arbitrary small,
which is not the same as zero.

Would you agree that the finite approximation 0.3333...3 (n threes) is
_not_
equal to 1/3, no matter how large n?

No. Any such finite approximation can be equal to 1/3, depending on the
error allowed in equality. (Absolute rigour is a phantom)

Alright... Who gets to choose the precision, and who is to be the
arbiter if there are discrepancies between, say, you and me? Also, is
zero error theoretically allowable in your system?

An error can be zero with integer (discrete) values, but not with reals.
Since an error can be arbitrary small, there is no "arbiter" necessary.
I've just changed your "for _all_ epsilon" into my "for _any_ epsilon",
thereby avoiding the _absolute_ rigour, but not the rigour.

I'll leave the rest for later.

Han de Bruijn

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