Near and far vs. big and small

[AntonioLao]

The number distances between rationals and irrationals are nearly infinitesimal yet an infinite numbers of irrationals fit between. The ratio of unity over infinity can be defined as the whole number zero but the ratio of unity over zero still not defined in mathematics. The distribution of primes along the real number line defies logical understanding yet no one can easily deny their existence. As Cantor asserted and proved a long, long time ago in our Milky Way galaxy that the infinity of the rationals is the same as the infinity of the fractionals but the infinity of the irrationals is bigger that both and yet less than aleph 1, which in turn is less than aleph 2, this is less than aleph 3, and so on, ad infinitum as properties of all transfinite numbers. These do not deter some modern mathematicians from believing the existence of the omega point of absolute infinity. But the Continuum Hypothesis still could not be proved at this time.

[Guille]

In fact, I don't understand why we say 2 goes after 1 and 3 after 2 and so on. There are infinite numberse in between each number (unlesss you write period and whole (for example, 0.999....(period) and 1 have nothing in between)).

By the way, how can an infinity of irratioanl numbers be bigger than the infinity of rational or fractional numbers if infinity is NOT a quantity?

[AntonioLao]

By the way, how can an infinity of irratioanl numbers be bigger than the infinity of rational or fractional numbers if infinity is NOT a quantity?

knowing the answer is what differentiate a mathematician from a non-mathematician. I consider myself as a non-mathematician.

[SinJin]

I think our concept of counting tries to create manageble units out of basically infinity. That's why a lot of problems or wierd paradoxes may occure. I also think this mimics our existence and the universe's, and may be tied with the TOE.

[Guille]

I think our concept of counting tries to create manageble units out of basically infinity. That's why a lot of problems or wierd paradoxes may occure. I also think this mimics our existence and the universe's, and may be tied with the TOE.

The problem is that we probably in the begining didn't have fractals, only whole natural numbers, but this changed and we realised soon that there are infinite number in between because in nature we can also see these fractals: 1 apple, 2 apples, 3 apples, but you eat half of the 4rth apple. Thus, you have 3.5 apples. Nature gave us perception, and we percieve what we want.

[MostConducive]

You (Original Poster) said "unity over Infinity" is (or could be defined as) the whole number Zero. I take issue. First of all, I believe Unity Over Infinity is The Infinitesimal, and there can be only one such entity (how could there be another real infinite oneness? they'd collapse logically, just as 'being in itself' collapses ontologically). I suggest the fundamental nature of the Infinitesimal (as the limit in itself, not a variable but a fixed constant, even the principle) is that 'There Can Be Only One' to quote the Highlander, as it would be for the unicity of units, for the true and transcendental (integral) Unity. Thus, I declare it be be justified rigorously that it is the Origin (I agree with that) which is not Zero but One, good plain old One. Besides, Zero is not a number, just as non-being doesn't exist, and this is for the same reason as Infinity itself being not a quantity (nor a mode of quantity such as number), such a quantity is not infinite but (rigorously) indefinite. So-called 'Infinitesimals' (as Leibnitz used them for instance) are quantities of the variable domain 'indefinitely small,' not infinite. Unity Over Infinity, the Prima Ratio is the Infinitesimal, it is One, being itself, oneself, the Spirit which is the Alpha and Omega Point, not the Absolute Infinite. The Absolute Infinite is Ultimate Reality, but the distinction between this and Pen-Ultimate Reality is the Infinitesimal which is Unity, the first and last of all number and counting, the first one and the last one.

[gautam]

Repetitive may I sound but I would say that sooner or later we haveto take into account what I have explained in my MEST theory ,the small scale infinity which exists between any two scales or points or numbers, small or big. That explains the continuum. Numbers are nothing but our own creation. We cant understand anything in its completeness or absoluteness. We need to break every thing to analsye and grasp. We cant therefore thrust our own limitation on the reality.When we do that it distorts the latter. 1 can be half ,it can be full it can also be infinite, depending on the perspective. But it can never be zero.

[Lloyd Gillespie]

Antonio, have you ever considered the fact that infintessimal numbers exist, or at least could be created, beyond any possible reality, even infinity? Numbers, improperly used, are the curse of humanity... We need a new 'whole math' based on real, new and super-rational definitions of 1, 0 and infinity... Is this possible?

Regards,
Lloyd

The number distances between rationals and irrationals are nearly infinitesimal yet an infinite numbers of irrationals fit between. The ratio of unity over infinity can be defined as the whole number zero but the ratio of unity over zero still not defined in mathematics. The distribution of primes along the real number line defies logical understanding yet no one can easily deny their existence. As Cantor asserted and proved a long, long time ago in our Milky Way galaxy that the infinity of the rationals is the same as the infinity of the fractionals but the infinity of the irrationals is bigger that both and yet less than aleph 1, which in turn is less than aleph 2, this is less than aleph 3, and so on, ad infinitum as properties of all transfinite numbers. These do not deter some modern mathematicians from believing the existence of the omega point of absolute infinity. But the Continuum Hypothesis still could not be proved at this time.

[MostConducive]

I haven't read your MEST theory, I'll check it out. This continuum is four dimensional, and thus we have fivel levels of eternity, counting level zero as the absolute. The first level is the Infinitesimal... Analytically, variables may be defined as infinitesimals, but such plurality only exists as fictions, and cannot be integral, cannot be realized in such contradistinction to each other. There is one Infinitesimal, and it is ever-present.

Infinity is not scalable. Infinity is not quantifyable, and any such 'small-scale infinity' is merely an indefinite. The only fixity or constance of Infinity is its Absolute nature, its ultimate reality.

To break everything is the nature of analysis, but the continuum is not a set of infinite points, its as absurd as the self-contradiction 'infinite number.' How can you break the point of perspectivity behind the self? You cannot, because it is the transcendental operation of integration, the metaphysical 'realization' of the entity. That realization is the nature of the continuum.

Zero is not a (whole) number. The first whole is one, and its is the point of departure for all numbers.

[AntonioLao]

We need a new 'whole math' based on real, new and super-rational definitions of 1, 0 and infinity... Is this possible?

How about just 1 and -1?