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**Author:**

Leon, Antonio

**Category:**

Research Papers

**Sub-Category:**

Mathematics and Applied Mathematics

**Language:**

English

**Date Published:**

November 30, 2023

**Downloads:**

107

**Keywords:**

N/A

**Abstract:**

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

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.

He should now understand that he does not know how to handle infinity.

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.

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.

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.

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