New whole numbers classification

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3 minutes ago, studiot said:

Yes, butit is also true that many ( actually an infinity) other classifications are possible.

So how is yours useful?

Please, sorry to repeat again and again: read the entire article carefully.

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Maybe you should answer questions, instead of referring back to people reading your article. Assume they have, and if they still have questions answer them, or direct them, with a lot of help and all the necessary steps, to the right answer.

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45 minutes ago, Dagl1 said:

Maybe you should answer questions, instead of referring back to people reading your article. Assume they have, and if they still have questions answer them, or direct them, with a lot of help and all the necessary steps, to the right answer.

I logged on just to say +1 for this.

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2 hours ago, Jean-Yves BOULAY said:

When I said: 0, 1 and all primes not admit any non-trivial divisor (whole number) being less than them. Why are You so afraid of this? So also answer this question: is it right or not? If this is true then the whole numbers divides well into two groups: ultimate and non-ultimate numbers.

Your definition is fine. It defines exactly what you want it to define: what we get by adding 0 and 1 to the primes.

But you lie when you state that the whole numbers are not divided into two disjoint classes, primes and non-primes (the expressions themselves actually say that much). This sounds like it is a motivation for being interested in your new study object, that you claim has a superior property, does it not? Therefore as soon as we see that you are wrong, which is very soon, we should have to lose interest. How is that a good thing for you, do you think?

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6 hours ago, taeto said:

And why so-called prime numbers? I do not know how it works in French, but you should realize that this sounds insulting. You should remove such phrases from your paper if you want to be taken seriously.

"so-called" is in sens "thus called"

1 hour ago, taeto said:

Your definition is fine. It defines exactly what you want it to define: what we get by adding 0 and 1 to the primes.

But you lie when you state that the whole numbers are not divided into two disjoint classes, primes and non-primes (the expressions themselves actually say that much). This sounds like it is a motivation for being interested in your new study object, that you claim has a superior property, does it not? Therefore as soon as we see that you are wrong, which is very soon, we should have to lose interest. How is that a good thing for you, do you think?

The association of the numbers 0 and 1 with the primes, then the distinction of 4 classes of numbers, allows many arithmetic singularities.

3/2 ratio, this term appears hundreds of times in this article! It is always involved between and in sets of entities of 5x sizes (so 3x + 2x) including, in most situations, various matrices of ten by ten entities. These arithmetic phenomena demonstrate the equality of importance of the different types of entities studied as the ultimates or non-ultimates, the primordials or non-primordials, the digit numbers or non-digit numbers among the fundamentals, the numbers of extreme classes and those of median classes, fertile or sterile numbers, etc. . Thus is revealed in this article quantity of dualities distinguishing whole numbers in always pairs of subsets opposing in various ratios of exact value 3/2 or, more incidentally, of exact value 1/1.

Also, many of the phenomena presented, in addition to involving this arithmetic ratio of 3/2, revolve around the remarkable identity (a + b)2 = a2 + 2ab + b2 where a and b have the values 3 and 2. This generates many entanglement in the arithmetic arrangements operating between the different entities considered and therefore strengthens their credibility by the dimensional amplification of these arithmetic phenomena.

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You answer "so-called" means "thus-called". Which aligns with what Strange said.

But your text would change into having a paragraph starting: Until now, the definition of thus-called prime numbers did not allow etc.

So then this newly added "thus" does not refer to anything previous. This language problem persists, and you have to revise your text for certain parts of it to make sense.

And did you think about $$15\times 15$$ matrices? And do you actually not think that the corresponding $$5\times 5$$ matrices would make a good introduction for beginners too?

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7 minutes ago, taeto said:

You answer "so-called" means "thus-called". Which aligns with what Strange said.

But your text would change into having a paragraph starting: Until now, the definition of thus-called prime numbers did not allow etc.

So then this newly added "thus" does not refer to anything previous. This language problem persists, and you have to revise your text for certain parts of it to make sense.

And did you think about 15×15 matrices? And do you actually not think that the corresponding 5×5 matrices would make a good introduction for beginners too?

I have worked on other matrices but there are more significant results with matrices to 10 by 10. But see above there is also with 5 by 5. "so-called, "thus-called" these grammatical problems are secondary.

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3 minutes ago, Jean-Yves BOULAY said:

I have worked on other matrices but there are more significant results with matrices to 10 by 10. But see above there is also with 5 by 5. "so-called, "thus-called" these grammatical problems are secondary.

You choose $$10\times 10$$ because the results are more significant than for other sizes?

Would you be able to explain exactly how the results for, say, $$7\times 7$$ matrices are not as significant as for $$10\times 10$$ matrices? So we can at least understand what you mean by a "result" and how to rate its significance.

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17 minutes ago, Jean-Yves BOULAY said:

I have worked on other matrices but there are more significant results with matrices to 10 by 10.

Maybe that means it is just chance that some relation appears to hold for small numbers. If it doesn't generalise to all integers, then maybe it is not too meaningful.

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1 hour ago, Strange said:

Maybe that means it is just chance that some relation appears to hold for small numbers. If it doesn't generalise to all integers, then maybe it is not too meaningful.

In my introductions and conclusions I insist that these phenomena are related to the decimal system and therefore to small closed matrices of 5x or 10x entities. This is the basis of the article which does not study long sequences but their start (in multiples of 10 or 5).

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1 hour ago, Jean-Yves BOULAY said:

In my introductions and conclusions I insist that these phenomena are related to the decimal system and therefore to small closed matrices of 5x or 10x entities. This is the basis of the article which does not study long sequences but their start (in multiples of 10 or 5).

It is clear that you did a lot of work just on the $$10\times 10$$ case.

Maybe you did much less work on the $$n\times n$$ cases for $$n < 10$$ or $$n > 10$$. What is your feeling about what happens if you consider one of those other cases? Say, for $$n = 20,$$ maybe the typical relationship will no longer be 3:2 or 2:3, but maybe 5:2 or 2:5.

Will you continue to study these more general cases, or will you encourage somebody else to continue your studies?

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1 hour ago, taeto said:

Will you continue to study these more general cases, or will you encourage somebody else to continue your studies?

I obviously encourage anyone to explore further beyond. My article is only the beginning in this way and I work myself (and I have already discovered) on other phenomena including especially with the concept of Sophie Germain numbers.

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Inclusive diagram of the new whole numbers classification.

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Initial arithmetic arrangements in 3/2 ratios inside hierarchical classification of whole numbers.

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