Re: Bruijn babbles bull***

On Feb 4, 5:55 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:
Aatu Koskensilta wrote:
On 2008-02-04, in sci.math, Han de Bruijn wrote:

We don't know. Read my lips: we don't know.

What does our knowing or not knowing have to do with the existence of
a run of nines in the decimal expansion of this or that real?

We don't even _have_ THE decimal expansion of this or that real.
We only have _a_ decimal expansion of this or that real.
And you know it. So what does your "existence" mean then?

It's your predicate, you choose. Nine9s(x) means:
(a) The base-10 representation of x does not terminate
(in which case it is unique) and it contains a sequence
of nine 9s, or

(b) If the base-10 representation of x terminates (in all 0's),
then there is a run of nine 9's in it.

(b') The base-10 representation of x terminates, and therefore
Nine9s(x) is true because x has a representation terminating
in all 9s.

Your predicate either means (a) or (b), or it means
(a) or (b'). What's the problem with that? You have
complete freedom to choose the meaning.

We could also say "by base-10 representation we mean
representations that do not end in all 9's", in which
case all representations are unique. Then once again
every real has THE decimal representation.

- Randy
.