Talk:Karatsuba phenomenon

First line, Third paragraph
I'm trying to help on this page, but can't quite make sense of what is meant by the following statement.
 * "If to consider the numbers having even and, correspondingly, odd amount of prime factors in their canonic representation, then the amount of the first and of the second ones between all natural numbers is approximately the same"

Anybody know what the author meant? Cliff (talk) 14:48, 19 August 2011 (UTC)

I am sorry, if you believe that you help, writing: If one counts natural numbers up to some given limit, distinguishing those that have even respectively odd numbers of prime factors in their prime factorization, then the amount of both kinds will always be approximately the same. If instead one only counts those numbers whose prime factorization contains no primes belonging to a given arithmetical progression (for instance, no primes congruent to 1 modulo 6), then the picture will be another one: the number of cases with an even number of prime factors will be less than those with odd number of prime factors. ? --- you are wrong! What is "the given limit" if "one counts natural numbers"? Are you a specialist in number theory? I am sure --- you are not! What expression you don't like in the previous text? "Canonic representation"? It's a widely used expression. If you believe that the author is wrong, please, read the book and papers by Edmund Landau, the author "meant" the same that "meant" Landau. If you don't understand what means "the amount of the first and of the second ones between all natural numbers is approximately the same", then this expression is written as a formula below $$ n_1(x)-n_0(x)=O\left(xe^{-c\sqrt{\ln x}}\right). $$

You "improved" the text deleting mathematically literate text, and introducing absoultely illiterate text. Why you mentioned the factorization and the fundamental theorem of arithmetic, what for? What do you believe, if it would be not "the fundamental theorem of arithmetic", the natural numbers (positive integers) wouldn't have prime factors? Somebody mentioned the unique representation? You even didn't notice, that we have business with asymptotics!

I can not understand the Wikipedia politics: why they permit to edit texts to the people who are not specialists in the fields! I will delete your "improvements" --- I don't know where you are living, if in U.S.A., please, come to Hugh Montgomery or Enrico Bombieri, they will explain you what meant the author of this topic.91.78.176.112 (talk) 21:31, 23 August 2011 (UTC)

I returned to the previous text. May be, it's not so good in English, but it's good in math, at least. Please, respect the work of the specialist, not an amateur !91.78.176.112 (talk) 21:38, 23 August 2011 (UTC)


 * This is precisely the problem—your English is quite difficult to understand. Do not be offended when we try to improve the clarity of your English sentences. If the English text is confusing or ambiguous, you cannot justify a claim that it is "good in math". Thank you, however, for providing a clear explanation of what you mean in the form of a mathematical formula. That is much easier to understand than your English, and having that will allow us to improve your sentences so that they are clear. —Bkell (talk) 23:03, 23 August 2011 (UTC)

I changed the expression "natural number" to "positive integers" in some cases, also the "amount" to "number". May be, it will sound better?91.78.176.112 (talk) 21:47, 23 August 2011 (UTC)