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.