All Porton's Blog Messages

Below is how I have responded to a comment by some Trent to this my post:

I think that you are a mad person... psychotropic weapons, reliance on personal revelations, virtual marriage with president's daughter...

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I significantly updated online article Category of Endomorphisms and Pseudomorphisms. (Updates concern mainly projection of a morphism and being generalized for precategories rather than only categories.) It is a base for my theory of formulas.

I suggest to add it to the base math University program (see also here).

This is nearly the final draft, the state in which this article will be published in Journal of post-Axiomatic Mathematics and Logic (to be used as a base for other articles) and will go to preprint and/or paper publication (when will be converted from an XML format to LaTeX).

New online math journal Journal of post-Axiomatic Mathematics and Logic is expected to start its activity soon. The journal will publish materials related to definitional and functional methods in math logic intended to replace axiomatic method (20 century mathematics) with 21 century post-axiomatic mathematics, as well as research concerning theory of formulas and related issues (see here and here for details).

First articles for the journal are near to be ready for publication. Please donate for publication of this mathematical journal and development of PostScript/PDF conversion tools associated with XSLT stylesheets for math (which will be free available for use by other math journals and math Web sites) and for development of the stylesheets themselves. Articles are planned to be available free of charge.

www.mathematics21.org

My category theory terminology page is updated. The most important changes: fixed error in definition of a category, added notion of trans-endomorphism used to define a typed morphism in an elegant way.

I suggest to use my variant of category theory terminology instead of the standard category theory definitions as found in math encyclopedias.

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I published online my definitions of basic category theory terms (category, precategory, functor, prefunctor, morphism, etc.) with some simple theorems about them. My definitions differ of the standard encyclopedic definitions. I suggest to use my definitions for any serious math research instead of the standard definitions. (I use my definitions for http://www.mathematics21.org/category-theory.html">my category theory research.)

Additionally, I have elegantly defined a category based on a semigroup.

В Библии написано Если исповедуем наши грехи, Бог, будучи верен и праведен, очистит нас от всякой неправедности. Потому я исповедую об одном нашем грехе (связаном с аномальным явлением):

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Please donate for revolutionary math research (both fundamental and practical). donate for 21 century mathematics!

Now accepting credit cards (VISA and MC) as well as checks, e-gold, MoneyBookers, etc.

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Please donate for biblical Christian ministry. The ministry is based on 100% belief in Bible truth and is intended to reveal and teach the mysteries of Bible, the God's Word.

Now accepting credit cards (VISA and MC) as well as checks, e-gold, MoneyBookers, etc.

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All search engine companies, please take attention to correctly index math on the Web!

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I have responded to a business offer to me with a madness of preaching!

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Были замечательные кондитерские рулеты "Торнадо" (примерно 20 см в длину). [Верните их в торговлю!]

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In this small article I define inverse image of a category by a function and analyse its simple properties.

It is used in category theory research.

(1Tim. 4:1) But the Spirit says expressly that in later times some will fall away from the faith, paying attention to seducing spirits and doctrines of demons.

People often base their religious teaching about demons (demonology) on sayings of demons themselves. It is a wrong way, because demons lie or tempt.

However in modern Christianity (later times) many demonologists have started to base their teaching about demons on reversing what demons say. They think that if a demon says something then the truth is the reverse.

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В прошлом я нередко устраивал провокации, а именно провоцировал кого-нибудь напасть на меня же самого. Я таким образом надеялся, что, например, это станет известно милиции и мне заплатят компенсацию.

Вот пример для сравнения: Положим, к тебе подходит человек с ножем. Один из вполне естественных и довольно разумных вариантов - сказать ему Нападай! Так, во всяком случае, можно попытаться установить определенное, выгодное для тебя, время атаки. Дает ли твое предложение напасть на тебя ему право на нападение? Конечно, нет.

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I have updated my article where I doubt whether all other people except of me will go to the hell in he case if it will happen that I will be in conflict with people and not in communication with them, e.g. would become unable to communicate because of a failure to pay for Interet access, based on certain Bible verses.

It is not a humor, I raise a serious theological problem, and if you know anything about biblical concept of salvation, I welcome you to discuss this issue or to say your opinion. Are there any theologist among the entire World (well, Church) which has wisdom to solve this complex problem?

I have an idea how to cleanse cities from the dirty stain. Probably a very stupid idea, but maybe it is good idea, I do not know; I can't calculate economical aspects, etc. Make machines which will produce big number of soap bubbles, like children do but in much greater quantities.

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Traditionally many scientists deem that there are no life after death. However if think a little it becomes quite evident from the scientific viewpoint that after death remains something (outer space radio waves remaining from electromagnetic activity of a living body, for instance). The question is not whether somethings remains after death but whether this something continues to life (think, take decisions, communicate with others, etc.) or not.

But if to think yet a little it also becomes evident that in the infinitely complex nature at least some of combinations of spectral components of the radio waves, which may remain after death of a man, behave like a living creature. Remember the famous example of 1000000 monkeys randomly pressing keyboard keys? If they would do it unlimited time, they will type something reasonable. That is if we have an unlimited number even of random variants, some of the variants will be reasonable (alive). Likewise because there are infinite number of combinations of spectral components of radio waves, some of them will be alive, as out of infinite number of combinations some will happen to be alive.

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Theorem. Let f and g are binary relations. Then the following statements are equivalent:

1. g = f|_{dom g}.
2. Exists a set K such that g = f|_K.
3. gg^-1 = fg^-1 and g is a subset of f.
4. gg^-1 = gf^-1 and g is a subset of f.
5. gg^-1 = fg^-1 and dom g is a subset of dom f.
6. gg^-1 = gf^-1 and dom g is a subset of dom f.

An other, a little less convenient for usage but much easier to remember (mnemonic), equivalent form of this theorem is:

Theorem (mnemonic form). Given that f and g are binary relations and dom g is a subset of dom f, right multiplying (composing) both sides of the equation g = f|_{dom g} with g^-1 produces a formula equivalent to this equation.

I have stated this theorem as a conjecture in this weblog post. Now I have proved it. (The proof is below.)

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