Re: Well Ordering the Reals

Tony Orlow wrote:
>> It seems that the general approach is essentially to define multiple digital
>> points. With normal finite digital numbers, all significant digits are within a
>> finite number of steps of THE digital point at bit 0, and that's how we know
>> their values. I guess what my system really boils down to is defining multiple
>> digital points, at locations infinitely far apart in the string, with finite
>> neighborhoods.
>>
>> When I say 1:000...000 is N, that colon is a digital point at log2(N).
>

William Hughes wrote:
> What is a your definition of a finite neighborhood?
> So how far is the last 0 in 1:000...000 from the digital point?

More questions for Tony:
When you write x = 0:100...000, and you say that the "..." represents
an infinite number of zero bits, you appear to be definining a number
with an infinite number of low zero bits "...000" and three extra high
bits "100" positioned past the last infinitely-positioned low zero bit.

It looks x is composed of oo+3 bits. Or does the "..." represent only
oo-3 bits? What is 3 bits shy of infinity?

.

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