Re: Relative Cardinality

mueckenh@xxxxxxxxxxxxxxxxx writes:

> Virgil wrote:
>> In article <1120993982.779060.290210@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>> mueckenh@xxxxxxxxxxxxxxxxx wrote:
>>
>> > Randy Poe wrote:
>> >
>> > > > It cannot be distinguished from all other numbers.
>> > >
>> > > Of course it can. All numbers which are not equal to
>> > > sqrt(2) are either larger than it or smaller than it,
>> > > are distinguished from it, and are separated from it
>> > > by a nonzero amount.
>> >
>> > Like 0.999... and 1.000... are separated by a non-zero amount? Or is it
>> > a larger amount? How much more is it? Please specify.
>>
>> Does WM claim that 0.999... and 1.000... represent different real
>> numbers? Then WM should be able to specify their difference.
>
> As long as we consider digits which are enumerated by natural numbers,
> these different representations represent different numbers in fact.
> Their difference is 1/n for any arbitrarily large n, but it is not
> zero.

Nope. Their difference is _smaller_ (or equal) than 1/n for
arbitrarily large n, and it is greater than or equal than 0. That
makes it 0 exactly.

You again get your quantifiers confused in an appalling way, which
makes for completely nonsensical claims of yours. The difference of
two numbers not depending on n can't depend on n.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum
.

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