Date: Mar 5, 2014 12:08 AM
Subject: Re: Infinity: The Story So Far
On 3/4/2014 8:58 PM, Ross A. Finlayson wrote:
> On 3/4/2014 8:22 PM, Dan Christensen wrote:
>> On Tuesday, March 4, 2014 6:31:59 PM UTC-5, Dan Christensen wrote:
>>> On Tuesday, March 4, 2014 6:05:43 PM UTC-5, John Gabriel wrote:
>>>> On Tuesday, 4 March 2014 21:04:22 UTC+2, Dan Christensen wrote:
>>>>> It is an essential property of the natural numbers: there exists at
>>>>> least one element of N.
>>>> It has nothing to do with natural numbers.
>>> Well, you go ahead play around with number systems without any actual
>>> numbers in them, and see how far you get, John Gabriel. Sounds really
>>> boring to me.
>> Note, too, that the only constants you give in your "axioms" are a '0'
>> and something called a "unit". Unlike the case with the Peano axioms,
>> nowhere are these constants called numbers. Why is that, John Gabriel?
>> The only way to create new numbers is applying difference, sum,
>> reciprocal and multiply operators to existing numbers. If you start
>> with no numbers, you cannot generate new ones even if these operators
>> were well-defined -- which, as we have seen here, they are not.
>> So, good luck trying to derive any number-theoretic results whatsoever
>> from these Gobbledygook Axioms of yours, John Gabriel.
>> Download my DC Proof 2.0 software at http://www.dcproof.com
>> Visit my new math blog at http://www.dcproof.wordpress.com
> Aw, lighten up, DC, as we care at least it can be gone about whether
> or not JG goes about it.
> I'm interested in your experiences writing theorem provers as there
> is much to it.
> The thing is, shattered apart and through a kaleidoscope, JG's
> statements can at least in part be assembled in a form of sense.
> The plain declaration of the structural components, then has that
> any mutually co-existing structures simple are, as each is. Then,
> there are pointed out facts in the development that could be useful
> in general methods for usual collections of data and these are
> called Newton-Cotes relations. Then, insofar as that surprises
> people, as it seems a striking feature that would be noted, when
> reduced to the context, and rather reduced in the context, it is
> composed of other striking features of the numbers and geometry.
> These are so composed as to the striking foundations. Where he's
> deceptive if simply in omission, it's as simple to see that as
> omission. What that means is that these are some un-obvious, if not
> unclear, features that JG would value as information, that in
> establishing priority, it would be of him to develop something that
> would deserve a primacy.
> The kaleidoscope here is the entertaining device of pre-electronic
> days that with a rotating barrel tumbled pieces of colorful glass
> where the eyepiece through the kaleidoscope then had mirrors in the
> construction, of beautiful symmetrical patterns as snowflakes when
> seen to the light.
> These days a kaleidoscope probably cost more than your iPod.
And we had to spell all our own words.