Science Journals

All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident: Arthur Schopenhauer -- In questions of science the authority of a thousand is not worth the humble reasoning of a single individual: Galileo Galilei -- Science is a wonderful thing if one does not have to earn one's living at it: Albert Einstein -- When you have eliminated the impossible, what ever remains, however improbable must be the truth: Sir Arthur Conan Doyle -- We all agree that your theory is crazy, but is it crazy enough? Niels Bohr -- Whenever a true theory appears, it will be its own evidence. Its test is that it will explain all phenomena: Ralph Waldo Emerson -- Since the mathematicians invaded Relativity, I do not understand it myself anymore: Albert Einstein -- I would say that the aether is a medium invented by man for the purpose of propagating his misconceptions from one place to another: W.F.G. Swann: -- Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone: Albert Einstein -- Physics is mathematical not because we know so much about the physical world, but because we know so little: Bertrand Russell -- If I could explain it to the average person, I would not have been worth the Nobel Prize: R. P. Feynman -- I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use: Galileo Galilei -- How dare we speak of the laws of chance? Is not chance the antithesis of all law?: Bertrand Russell -- Only two things are infinite, the universe and human stupidity, and I´m not sure about the former: Albert Einstein -- The glory of mathematics is that you don't have to say what you are talking about: Richard Feynman -- Anything is possible if you don´t know what you are talking about: Author Unknown -- In life, everything is relative - except Einstein´s theory: Leonid S. Sukhorukov -- Don´\'t worry about people stealing your ideas. If your ideas are any good, you´ll have to ram them down people´s throats: Howard Aiken --A day will come undoubtedly when the ether will be discarded as useless: H. Poincaré -- First they tell you you´re wrong and they can prove it; then they tell you you´re right but it isn´t important; then they tell you it´s important but they knew it all along: Charles Kettering -- It is not once nor twice but times without number that the same ideas make their appearance in the world: Aristotle -- The opposite of a true statement is a false statement. The opposite of a profound truth may well be another profound truth: Niels Bohr -- A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it: Max Planck -- Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions: Eric Temple Bell -- Half this game is ninety percent mental: Yogi Berra

Arithmetic singularities of aleph-null

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

September 9, 2020

File:

/Research Papers-Mathematics and Applied Mathematics/Download/8394

Downloads:

Keywords:

transfinite addition, transfinite multiplication, transfinite exponentiation, aleph-null, power of the continuum.

Abstract:

By means of orthodox transfinite arithmetic, this chapter proves, among other results, an unexpected inconsistency involving aleph-null and the power of the continuum.