Set Theory and Logic

1703 Submissions

[4] viXra:1703.0280 [pdf] submitted on 2017-03-29 22:47:37

The Infinitesimal Error

Authors: Igor Hrncic
Comments: 6 Pages.

Unfortunately, Cantor was wrong. His notion of transfinite bijection is flawed. Cantor introduced this notion of transfinite bijection as the additional axiom, even though without even realising this. From this error, other errors sprung into the existence. He did all this in the heroic effort to justify the death of infinitesimals, even though he wasn't aware of this either. Cantor went bravely on to defend the established error in higher mathematics before his mentors and peers who banished infinitesimals. Instead, he demonstrated the error of it. He never realised this as well. This paper elucidates this link between Cantor's errors and infinitesimals.
Category: Set Theory and Logic

[3] viXra:1703.0113 [pdf] submitted on 2017-03-13 04:06:52

Failure of the Diagonal Argument

Authors: Wolfgang Mückenheim
Comments: 3 Pages.

It is shown that Cantor's diagonal argument fails because either there is no actual infinity and hence no defined diagonal number or there is actual infinity but the diagonal number cannot be distinguished from all real numbers of the Cantor list. Further it is shown by another argument that there are not uncountably many paths in the complete infinite Binary Tree.
Category: Set Theory and Logic

[2] viXra:1703.0112 [pdf] submitted on 2017-03-13 04:15:07

Set Theory or Slipper Animalcule: Who Wins?

Authors: Wolfgang Mückenheim
Comments: 3 Pages.

Limits of sequences of sets required to define infinite bijections do not only raise paradoxes but cause self-contradictory results.
Category: Set Theory and Logic

[1] viXra:1703.0032 [pdf] replaced on 2017-03-06 04:56:10

The Union is not the Limit.

Authors: Wolfgang Mückenheim
Comments: 5 Pages.

Contrary to the assumptions of transfinite set theory, limit and union of infinite sequences of sets differ.
Category: Set Theory and Logic