Re: Well Ordering the Reals
- From: "David R Tribble" <david@xxxxxxxxxxx>
- Date: 30 Nov 2005 16:16:55 -0800
David R Tribble said:
>> I admit that I can't because I can't create a workable definition for
>> infinite numbers, so that addition, comparison, etc. work properly.
>> But your definitions so far are no better.
>
Tony Orlow wrote:
>> define x>y if the most significant digit where they differ is a 1 in x and a
>> 0 in y.
>
Virgil said:
>> But in TO's "infinite sequences of digits with two ends" how does one
>> tell which digit is most significant? TO keeps glossing over this
>> critical issue.
>
Tony Orlow wrote:
> As in all regular digital systems, the leftmost nonzero digit is most
> significant. You knew that.
But what about those infinite numbers that don't have a leftmost
nonzero digit? You know, those infinite numbers that are infinitely
long sequences of digits?
Two examples (which I gave in another post):
a = ...101010101010,
which is just '01' repeated forever, and
b = ...110110110110,
which is '110' repeated forever. Neither of these infinite numbers has
a most-significant digit, so we can't tell which one is larger by
comparing their "leftmost" digits.
Then there is the next problem of defining what it means to add
infinite numbers. What is a+b?
.
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