#03 True Geometry: the new modern meaning of infinity-- Space-filler,

Now in pages 1 and 2, I showed the reader the ugly contradiction at the heart of Geometry. The fact that a line has length and composed of only points, but that points cannot give a line length since points have no length. That is a contradiction and no mathematical subject can exist with a contradiction at its core.

The solution to the crisis of Geometry is to realize three entities exist, or three axioms are required and not just two, (1) points (2) line. We need a third axiom or entity to give lines length (or distance). This third entity is empty-space between two successive points. We achieve this empty- space by recognizing some points are finite-number points while other points of Space are infinity-number points.

In order to tell whether a point or a number is a finite-number or an infinity-number, we need to be logical persons, logical thinkers. We cannot be those rumdummies of the past history of mathematics who lacked the logic to do and understand this. Our ancestors failed on infinity and even our present day teachers failed on infinity. Because in order to have a concept of finite versus infinite, there must be a border between them. Now later on in this book I show several math proofs where that borderline lies which ends up being the very large number 1*10^603, but that is further ahead in reading, whereas here I want to explain to the newcomers.

Logic, logic, logic is the key to whether your math is true or whether your math is fakery. All will agree that finite and infinity are linked to one another. Yet in all the history of mathematics, no-one until 2011 ever insisted on a borderline between finite and infinity. So once you impose the requirement that whenever you mention the word "finite" or the word "infinite", you must be able to speak about the borderline between the two, otherwise, finite and infinite are just vague notions, not even mathematics.

Here we see in the Wikipedia entry of "infinity" this huge tussle and vagueness of what finite and infinite mean:

--- quoting Wikipedia on infinity ---

Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics. The English word infinity derives from Latin infinitas, which can be translated as "unboundedness", itself calqued from the Greek word apeiros, meaning "endless".[1]
In mathematics, "infinity" is often treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is not the same sort of number as the real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number. Georg Cantor formalized many ideas related to infinity and infinite sets during the lateÂ*19th and early 20thÂ*centuries.
--- end quote ---


Notice where they say "infinity often treated as though it were a number-- it counts or measures things; an infinite number of terms".

When you read the Wikipedia entry of infinity what you encounter is the modern day rumdummy understanding of infinity, an infinity and finite concepts without the borderline between them.

But the reader is smarter than all the mathematics professors and authors who endorse the above definition of infinity, an infinity without a border. For the reader senses that if you have a concept of finite, related to infinite, there must be some link or connector between the two to tell them apart, and that link or connector is a border between the two. That is just pure logic, not the senseless sentiment of rumdummies of Old Math.

So, let us pretend 10 is the last finite number and anything larger than 10 is an infinity-number. But we do not stop there, for if 10 was the last finite-number, that causes us to look at 1/10, which Wikipedia authors call the "infinitesimal". So if 10 is what I call Large infinity or macroinfinity, it causes 1/10 or 0.1 to be microinfinity. So in this Universe Space of mathematics where 10 is the macroinfinity borderline, causes there to be no finite-number between 0 and 0.1 and that Space I call empty-space between 0 and 0.1. It is not technically empty for it holds microinfinity numbers, none of which are finite numbers.
So in this Space, what is called the 10-Grid, all the finite numbers are 0, then .1 then .2 on up to 9.8 then 9.9 then 10. So in the 10-Grid the total number of finite-points is 101 when including 0. And everything else in that Space is infinity number points, as a filler of the Space.

So in mathematics, when you do it with Logic, and not rumdummy silliness, you want and need finite versus infinite. But that means you have to apply logic to tell you what number is a finite and what number is an infinite. That by logic, demands you find the borderline between finite and infinite.

Now what I have spoken mostly so far in this page is algebra and not geometry.

So let me dwell on Geometry for this finite versus infinite concepts. Space in Â*Euclidean Plane Geometry must have finite and infinite concepts for it has lines that go to infinity and finite lines. So therefore, Space must have a borderline between finite and thence infinite. Again, as I said previously, in a future page of this text we see where we pinpoint accurately this borderline and mathematics points to the number 1* 10^603.

So that means for Space and Geometry, that finite numbers are discrete and separated from one another by at least a distance of length of 1*10^-603 an infinitesimal length. And at 1*10^603 Space is just infinity-numbers for there on after.

Now in Old Fake Math what the Wikipedia entry on infinity is discussing, the meaning of infinity in that fake math is that of "endless or unbounded". That alone is hypocritical and contradictory. For the number 1/3 is thought to be finite, yet when written as 0.33333..... it is endless in 3 digits. So in Old Math, they were never good at using logic, never had a gram of logic to spare to see if their understanding makes sense or nonsense.

In New True Math, True Geometry, infinity has a more beautiful meaning, as a "space filler between successive finite points". Like on your clear plastic ruler where you have hash marks between centimeters and millimeters, of empty-space so that you can measure for length or distance. When you use a distance formula in Geometry such as the Pythagorean theorem, what you are measuring is the length or distance between points A and B where between A and B is empty space.

So in New True Math, we dispense with the old fakery of infinity being endless or boundless or other nonsense. In New True Math, infinity resides next to every finite point or finite number and where infinity at the last and largest finite number becomes a region of space where all the numbers or points are infinity and no finite points exist.

Now a special note to the reader, in that all the work of Cantor as mentioned in that Wikipedia page, all his work on infinity is pure rubbish, for Cantor never had the gram of logical intelligence to pursue the borderline between finite and infinite. So a caution warning to students that if you read Cantor's work, that his is math fakery.

--
Drexel's Math Forum has done an excellent search engine for author posts as seen he
http://mathforum.org/kb/profile.jspa?userID=499986

Now, the only decent search for AP posts on Google Newsgroups, is a search for for it brings up posts that are mostly authored by me and it brings up only about 250 posts. Whereas Drexel brings up nearly 8,000 AP posts. Old Google under Advanced Search
could bring up 20,000 of my authored posts but Google is deteriorating in search of old posts to the science newsgroups.

So the only search engine today doing author searches is Drexel.

All the other types of Google searches of AP are just top heavy in hate-spam posts due to search-engine-bombing practices by thousands of hatemongers who have nothing constructive to do in their lives but attack other people.

Funny, and I have to laugh here, for in the recent news of spying on Europe by USA, such a big fuss, whereas I want that sort of full recording of all of my posts to Usenet. I am hoping the spy agencies of the USA has recorded every last one of the posts that AP has posted to the Usenet and please keep up that spy activity. I have kept a personal archive and figure that in these 20 years of posting of say 5 posts per day makes 365 x 5 = 1825 times 20 = 36500. So roughly I have about 36,500 posts to Usenet in these past 20 years. I hope many computers and servers have all those 36,500 posts safely stored and please feel free to display them. Whereas Google is working in the exact opposite, by trying to hide or destroy them, or bias the listing of those author posts.

Archimedes Plutonium