Alex,
It's very easy to find such fragments:
Alex> Please give me an example of "complex continuous fragment, which would require an uncountable amount of math to specify".
Just open your eyes. Everything you see has an open-ended amount of complexity. What you see at one glance can be captured with a digital camera that has a finite number of pixels. But if you look closer, the number of pixels for the closer look is the same if you're using the same camera. But the fragment you're viewing now has a much finer resolution.
You could use more technology to get down to higher and higher resolutions. The only limit is determined by Planck's constant, which is the limit of uncertainty.
That's the physical limit. But the mathematical limit can go to arbitrary depths. Any fragment of an arbitrary function on a n-dimensional space is continuous. If you allow such fragments in your formalism, there is no limit to the depths you can select in theory. You can prove general theorems about the depths. But any physical example is limited by the technology.
The formalism for GEGs is specified in Section 3 of Excerpts234.pdf, which I attached to a previous note. Subsets of that have been implemented by my colleague Arun Majumdar. Versions of that description can be implemented with fragments that are limited to whatever resolution you computer can support.
The theory has no limits. But any limitation is limited to what a digital computer can represent. However, it might be possible to go farther if you use some kind of analog-digital hybrid.
John
From: "Alex Shkotin" <alex.shkotin@gmail.com>
Sent: 11/20/23 2:37 AM
To: ontolog-forum@googlegroups.com
Cc: CG <cg@lists.iccs-conference.org>, Peirce List <peirce-l@list.iupui.edu>
Subject: Re: [ontolog-forum] Diagrams as defined by C. S. Peirce
John,
I should read more about GEG.
Is it possible to put it into the computer?
Please give me an example of "complex continuous fragment, which would require an uncountable amount of math to specify".
Alex