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**Author:**

Leon, Antonio

**Category:**

Research Papers

**Sub-Category:**

Mathematics and Applied Mathematics

**Language:**

English

**Date Published:**

October 11, 2024

**Downloads:**

47

**Keywords:**

actual infinity, potential infinity, Theorem of the Actual Infinity, spacetime continuum, inconsistency of the infinite sets

**Abstract:**

Physics never questions the hypothesis of the actual infinity that underlies its mathematical language. This hypothesis, debated for more than 25 centuries, suddenly ceased to be discussed when it was axiomatically accepted (Axiom of Infinity) more than a century ago. Ironically, it was set theory, based on this very hypothesis, that provided the author with the tools to prove its formal inconsistency. This paper denounces the scarce echo of these proofs (some of which were published 16 years ago) and invites the reader to examine one of them, the shortest I have been able to develop. It also points out the extraordinary importance of this inconsistency in a large part of physics, especially in cosmological theories and those that make use of the spacetime continuum. The question, then, is inescapable: what can be done to get physics to consider the possibility of this inconsistency and its consequences?

You say:

"that once all possible <-comparisons* of x with the successive elements of Q_01 have been performed"

This is an incorrect statement because the <-comparisons* do not finish.

You actually say that yourself with the innite set {x/2, x/3, x/4 . . . } .

So your conclusion that

"the assumed actual infinity of the denumerable sets N and Q01, is inconsistent",

makes no sense.

And by the way. You don't mention it but the successive values of x are:

1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, ........

"that once all possible <-comparisons* of x with the successive elements of Q_01 have been performed"

This is an incorrect statement because the <-comparisons* do not finish.

You actually say that yourself with the innite set {x/2, x/3, x/4 . . . } .

So your conclusion that

"the assumed actual infinity of the denumerable sets N and Q01, is inconsistent",

makes no sense.

And by the way. You don't mention it but the successive values of x are:

1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, ........

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