Re: Cantor Confusion

On 12/7/2006 8:51 PM, Virgil wrote:
In article <4577F17F.7000005@xxxxxxxxxxxxxxxxxxx>,
Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> wrote:

Dedekind himself let the question open whether his cut belongs to the
left or the right side. He was also lacking insight.

Actually, Dedekind saw that it made no difference which way it went, as
long as one one was consistent about it. Those, like EB, who fail to see
what Dedekind saw are the ones lacking insight.

One one? Perhaps a typo.

Dedekind's lack of insight is obvious: He imagined exemplary rationals
like distinct points on the continuous line. On this basis he claimed to
be able to separate all points and all reals, respectively, into left
and right ones. While he may claim having defined a cut somewhere, he
cannot properly and directly attribute a belonging address.


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