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

The Shortest Proof of the Inconsistent Infinity


Leon, Antonio


Research Papers


Mathematics and Applied Mathematics



Date Published:

November 30, 2023






This article contains the shortest proof I have been able to develop (less than 300 words) of the inconsistency of the Axiom of Infinity.


J. Zwarts(Netherlands):
Would Antonio Leon give a reaction on my comment of last December ?
He should now understand that he does not know how to handle infinity.

Posted: January 09, 2024 @ 6:45:53 am
J. Zwarts(Netherlands):
It's easy to create a list of all rational numbers in (0,1) with first element.

Make the well-known list (from the squared scheme) of all numbers in Q (>0):
1/1 2/1 1/2 1/3 3/1 4/1 3/2 2/3 1/4 1/5 5/1 6/1 5/2 4/3 3/4 2/5 1/6 1/7 3/5 5/3 7/1 .......

and only select the numbers in (0,1):
1/2 1/3 2/3 1/4 1/5 3/4 2/5 1/6 1/7 3/5 .......

There is no need to require that the numbers in this list should be in their natural order !!
Of course: there is no smallest number.

Posted: December 21, 2023 @ 7:02:08 am
Steve Olah(Laguna Woods, United States):
If you can measure it, if you can count it, the measurement or count will never reach infinity. The only infinite distance is the size of the empty space outside of the Universe, in any direction. The number of Universes operating in that space could also be infinite.

Posted: November 30, 2023 @ 8:04:14 pm

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