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Number 10 is so unique as it forms Completeness in the Galois Field



 
 
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Old December 20th 13, 10:03 PM posted to sci.astro
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Default Number 10 is so unique as it forms Completeness in the Galois Field

Number 10 is so unique as it forms Completeness in the Galois Field theory #92 Specialness of 10 and 1, 10, 100, 10^3, . . 8th ed.: TRUE CALCULUS

Sorry, the requirements I wrote yesterday need a fourth requirement -- that of Completeness or allowing All Possible Digit Arrangements. The number 10 with the Decimal System is unique in this requirement and so I call the number 10 the Galois Field theory Completeness number. In other words, Field theory is dependent on the existence of the number 10 with its special attributes.

On Friday, December 20, 2013 12:13:05 AM UTC-6, Archimedes Plutonium wrote:
Alright, now some may think that the number 2 can serve as the Universal Inverse concomitant with being the Mathematical Inductor that the number 10 is.



So let us try out 2, the binary system instead of the decimal, to see if it can be inverse along with math inductor simultaneously.



So 2 as in base 2

0 = 0

1 = 1

2 = 10

3 = 11

4 = 100

5 = 101

6 = 110

7 = 111

8 = 1000

9 = 1001

10 = 1010



Can we have a inverse? Suppose 4 were infinity border then the inverse would be 1/100 (1/4) and then we would have 1/100, 10/100, 11/100, 100/100 as fractions. But there is a problem with this in that we have a binary-point rather than a decimal-point and we represent 1.5 of decimal as that of 1.10 as binary. But here we run into a huge problem with the zeroes rightward of the binary point. How are we to know whether it is 10 or 100 or 1000 to the rightward of the binary-point? In decimal, it matters not how many zeroes rightward for 1.5, but for binary it matters. So in binary, do we need two binary-points as that of 1.10. to distinguish it as 1.5?



Well, we can do that and admit that the binary system with 2 creates a simultaneous Inverse along with a Mathematical Inductor. So that 2 is a rival for 10 as that superspecial number.



However, we have two other requirements which only 10 passes and all other numbers fail.



Requirements:

1) Universal Inverse which delivers all the numbers of that system in a Mathematical Induction of the inverse, aside from 0.



2) the square root of the number is close to that of the value of pi



3) the number has a prime 5 so that phi is built of

(1+sqrt5)/2 = golden mean



Only the number 10 satisfies all three conditions.



AP


The number 10 is so special that it is the only number, the unique number in mathematics to form the Galois Completeness of the Field theory.

Yesterday I wrote:

But I missed the most important feature of completeness in that list.

We need to have every possible digit arrangement to have Completeness. The binary system or any other system, except Decimal system is unable to furnish completeness.

For example, the numbers 0.3, 0.33, 0.333 etc etc are unable to be furnished in binary or any other system, except for Decimal system.

3/10, 33/100, 333/1000

In binary or any other system except Decimal, you need more than one binary-point. In Decimal, you need only one decimal point. The Completeness of Decimal System is that every possible digit arrangement is represented below a Grid. So that for the 10 Grid in Decimal we have 0.1, 0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9.

In the binary, in 8 Grid we should have 0.1, 0.10., 0.11. , 0.100. , 0.101. , 0.110. , 0.111. but the trouble is obvious in that the requirement of two binary points so as to separate zeroes does not allow for the Completeness of All Possible Digit Arrangements that the Decimal System allows.

So only the number 10 allows a system of All Possible Digit Arrangements as the grids grow from 10 to 100 to 10^3 on up to infinity border.

--
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
for author, could bring up 20,000 of my authored posts but Google is deteriorating in quality of its searches, likely because AP likes an author search and Google does not want to appear as satisfying to anything that AP likes. If AP likes something, Google is quick to change or alter it.

So the only search engine today doing author searches is Drexel. Spacebanter is starting to do author archive lists. But Google is going in the opposite direction of making author archived posts almost impossible to retrieve.

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.

Now one person claims that Google's deteriorating quality in searches of science newsgroups is all due to "indexing". Well, that is a silly excuse in my opinion, because there is no indexing involved when one simply asks for a author search. No indexing involved if one wants only the pure raw complete list of all posts by a single author. And Google is called the best search engine of our times, yet I have to go to Drexel to see 8,000 of my posts of which I had posted 22,000 to 36,000 posts from 1993 to 2013. It is a shame that Drexel can display 8,000 while Google has a difficult time of displaying 250 of my authored posts. Where the premiere search engine of Google is outclassed by Drexel and even by Spacebanter.

Archimedes Plutonium
 




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