Date: Mar 5, 2014 12:08 AM Author: ross.finlayson@gmail.com 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.

>>

>> Dan

>> 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.