You have done your imagery very well. I will wait and see what comes next. — jgill
I suppose I see some sort of a way to move forward by taking a lattice graph over an area and allowing the number of vertices and edges to increase without bound leading to a countable number of points in the area. — jgill
But this would be inadequate regarding the reals. But you might be able to push into the irrationals some way. — jgill
So far it appears everything you have given is uninteresting from a math perspective. — jgill
I don't think you will get a reaction from anyone but me until you produce a plan moving forward from your images of edges, vertices and surfaces. What is your goal and how do you plan to proceed? — jgill
I don't think you will get a reaction from anyone but me — jgill
1. should be interesting. — jgill
Intuitionism math perhaps. — jgill
You have density, but then continuity is next...I thought you were defining these lines as continuous. Fundamental objects. — jgill
There's an important distinction between handwaving and BS. Handwaving involves vagueness or imprecision, where the core idea might be sound but lacks detail or rigor in its current form. BS, on the other hand, is fundamentally incorrect—an argument that doesn't hold up under scrutiny and lacks substance from the start. — keystone
Indeed, with the very first predicate 'is a continua' still not fully defined, you've piled on a big mess of more of undefined terminology and borrowing of infinitistic objects while you claim to eschew infinitistic mathematics. — TonesInDeepFreeze
1D analogue of the established term "planar diagram" — keystone
Please, give me a chance. — keystone
If your offer to help was sincere — keystone
I don't need to waste my time and energy on you. — TonesInDeepFreeze
It's ironic that you became distant right after I went back, carefully studied, and addressed your comments on topology. — keystone
You need to define "1D analogue of the established term "planar diagram"" in terms that don't presuppose any mathematics that you have not already defined and dervied finitistically and such that it justifies such verbiage as about "embedding in a circle". — TonesInDeepFreeze
You are a sinkhole. — TonesInDeepFreeze
Move on to 2. — jgill
Actually, I think you're the sinkhole. You seem to enjoy destructive conversations. — keystone
I see a mistake in your last figure, typo probably. And I assume -1/0 (meaningless) designates negative infinity, however you define that — jgill
I see nothing of interest so far. — jgill
I've been overlooking the fact that real numbers are typically defined as equivalence classes of Cauchy sequences, not just individual Cauchy sequences. — keystone
Cauchy sequences themselves are infinite sets. — TonesInDeepFreeze
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