Re: Bruijn babbles bull***

On Feb 4, 1:37 pm, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
Yeah, you're right. But that's not what I mean. What I mean is to find
_new_ decimals in the expansion of e.g. Pi every time again. And again,
because it's never ending. So there is _a_ (finite) decimal expansion
available, despite of the fact that  many of us imagine it as the first
portion of THE infinite decimal expansion. I would say that the latter
does not exist.

I don't get that. Can you explain (one more time)? I believe you said
that you accept the existence of N, _the_ set of integers. Is this
correct? In particular, if you and I apply the axioms (0 \in N; if n
\in N, then also s(n) \in N), do you agree that we end up with the
same model for the integers?

Do you accept _the_ set of prime numbers?

Do you accept the infinite expansion 0.3333... as an equivalent to the
ratio 1/3?
Would you agree that the finite approximation 0.3333...3 (n threes) is
_not_
equal to 1/3, no matter how large n?

Do you accept the existence of Champernowne's number
0.123456789101112131415161718192021...?
Would you agree that I can produce for you any digit you care to name
in the decimal expansion of this number?

Do you agree that pi exists?
Would you agree that I can produce for you any digit you care to name
in the decimal expansion of this number, given enough time and
resources?

.

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