James S Saint wrote:Ecmandu wrote:James S Saint wrote:Space has infA^6 first order points (or more precisely: 4/3 Pi*((infA^2)/2)^3) whereas

time only has infA^2 first order points.

That is an extremely significant difference, especially concerning why the universe has substance, "exists".

I don't think there are orders of infinity. I don't know how you came to this result, but I do know that if time and space are both infinite, there are not orders to them to that regard.

Are you saying that the completeness of a sequence is an order of infinity?

Say...

2,4,6,8,10,12,14,16,18,20,22,24,26,28.....

vs...

1,2,3,4,5,6,7,8,9,10,11,12,13,14, 15.....

Are you saying one set is twice as large as the other set?

In mathematics, infinity has both cardinalities and orders (exponential powers).

An infinite sequence can be greater or lesser than another and thus alter the

cardinality (de Georg Cantor) of the "relative greatness of its infinity".

But in addition to being merely greater or lesser, infinity can be raised to exponential powers, such as infA^2 (ref

Edward Hewitt, Hyperreal Numbers)

A line in space can be ordered into the "real number" set, thus having infA^2 points. But that is only one of 3 dimensions. By including the other two dimensions, that line becomes a plane with infA^4 points and then a cube of infA^6 points.

Those are the "first order" points because merely the real number set was used to number the original points (even though there are infA^6 of them, requiring a higher order to individually number the first order points). But between any two infinitesimals ("1/infA") can be an entirely new number set. Thus creating the range of "1/infA^2" up through infA^2 on a line. That constitutes a

second order point referencing system. And that pattern can be continued indefinitely to any higher order. Thus there is no "absolute highest order of infinity", no "absolute infinity", and interestingly no "absolute zero".

This is an excerpt from my introduction post to this site...

By definition of infinity, there is no highest order of infinity, and it is false that they cannot be counted... you can list any sequence with an algorithm... if the algorithm itself has infinite processing time, then there is no sequence. Cantor and Chaitin were wrong.

It's considered a mathematical proof ala Cantor from over 140 years ago that all of the real numbers cannot be counted...

I use a techinique called 1 dimensional flooding to show that all of the reals cannot be counted in one list with one dimension, which is differnt than Cantors diagonalization argument.

use the lists..

012345678910...

123456789101...

234567891011...

345678910111...

456789101112...

567891011121...

678910111213...

etc...

To do one dimensional flooding, you simply add an infinite list to each place in the previous infinite list...

024681012151...

036912151821...

048121620242...

051015202530...

When the list converges at infinity, there is no way to begin counting...

12345678910...

13579111315...

14812162024...

Because you never pass the zero's.

This is the proof that we cannot determine the limit of how much we can count.

Sorry forgot to add the disproof of Cantor's diagonalization argument...

Once you do one dimensional flooding, you have to expand to another dimension to keep listing the sequences... diagonals can be subsumed by a third dimension, say list 1.1, or list 5.7 etc... or a 4th dimension 1..1, 5..7, etc...

It's actually easy to absorb the diagonals by starting from the center and listing them from top to bottom in sequence using another dimension... what this means is that cantors proof that you cannot count all the reals is false. It also means that you cannot find the limit on what can be calculated!!!!!!!!! except that it cannot be everything!!!!!!!!!

Basically, James, what this means, is that there are no powers to infinity, each dimensional flooding is just as large as another dimensional flooding.