You're referring to this:Undefined said:No, the originating concept of Euclid's was a philosophical notion pure and simple. Read wiki if you don't believe me. Is was an abstract invention' of Euclid's own IMAGINATION,

In geometry, topology, and related branches of mathematics, a spatial point is aprimitive notionupon which other concepts may be defined.

Being a primitive notion means that they have no properties other than those that are derived from the axioms of the formal system in which they are used, i.e., they do not have volume, area, length, or any other higher-dimensional attribute. In Euclidean geometry, a common interpretation is that the concept of a point is meant to capture the notion of an object, with no properties, in a unique location in Euclidean space.

As stated by me and others several times, mathematics is not physical. Physics is physical. If you want to equate real with physical and claim that mathematics is unreal, that's your prerogative, but mathematics "really" exists. Where is it? Where do numbers come from and why do we bother to use them as labels for real physical objects?Undefined said:His UNREAL and UNPHYSICAL 'dimensionless point' starting 'entity' can only produced more UNREAL and UNPHYSICAL logics and 'entities', no matter whether you call the edifice of abstract unreal entities that flows from that starting unreal entity "Mathematics" or "Unreal Logics System" or anything else.

Why do we do it then? Why do we use "unreal" numbers to label things? Why would anyone say they own "one car"?Please disabuse yourself of the fantasy that just because we call that particular unreality-based construct "mathematics" that it somehow makes it 'real'.

But it is complete, Euclidean geometry is axiomatically closed; points, lines, and planes along with arbitrary coordinate systems describe reality very well. Let me quote someone I have a bit more faith in than you:"Describes reality very well" you say? BUT I and others point out: Such an unreal geometry/math construct ultimately predicated (as I have shown clearly more than once now, both here and elsewhere over the years) upon unreal infinite numbers/identities representing unreal dimensionless points, and which outputs all the "undefined", "undetermined", "infinite" construction from dimensionless abstract constituents, cannot be COMPLETE in any sense, neither in abstraction or reality.

Roger Penrose said:The ancients may not have regarded it as a physical theory at all, but that is indeed what it was: a sublime and superbly accurate theory of physical space -- and of the geometry of rigid bodies.

But numbers are abstractions, mathematics is abstract because that's what it deals with--abstract entities. Are you going to rework the whole of mathematics since Euclid, and what are you going to use instead of numbers?Undefined said:It's time that we reworked from scratch, from a real non-abstraction/non-philosophical 'starting point', so that the "mathematical reality" THEN WOULD be complete and consistent analytical model FOR the "physical reality".

But you intend to change that? I don't think you will, I don't think you can get around the fact that mathematics and physics are not, and never will be, the same thing.Mathematics AS IT IS NOW is NOT PHYSICS.

Sorry, I don't really understand any of that. If that's what your "ToE" will look like, I'd say not many other people will understand it either.From this you can deduce the meaning of 'reality terms' as I explained before, here and elsewhere in this context of maths and physics modeling/analysis axioms/postulates etc. Ultimately, the only real 'infinity' is the DIRECTIONAL POTENTIAL from which the ACTUALIZED DIRECTIONAL POTENTIAL lines of physical spatial energy-space EFFECTS and FEATURES arise and subside in without cease. The LIMITS of LOWER ORDER infinities hit the brick wall when the MINIMAL INFINITESIMAL OF PHYSICAL energy-space EFFECTIVENESS is encountered by the PROCESSES which determine/construct the energy-space features, dynamics and overall universal phenomenological set arising from directional potential of spatial dimensions which Chaos Theory shows will produce the REALIZED DIRECTIONAL POTENTIAL energy-space 'observables' we model and predict.

As for your reply to James R, and your claim that 1/3 is a division that "hasn't even started", can you do long division? Do you know what dividing 1 by 3 implies when you do it?

You know, you say "3 goes into 1.0 0.3 times with 0.1 remainder, then 3 goes into 0.10 0.03 times, etc".

So the implication is that you will get an unending string of 3s after the decimal point. Also that you won't need to actually keep dividing to conclude that 1/3 is equal to 0.333...

These are the only logical conclusions you can make; there is no room for "not yet done", or "incomplete". That is mathematical reality (logically consistent and no errors).

You would need to be quite unintelligent, or intentionally stupid, to see otherwise.