Set Theory and Logic

1803 Submissions

[4] viXra:1803.0318 [pdf] replaced on 2018-03-21 06:51:30

Refutation of Abductive Reasoning © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

Abductive logic of C.S. Peirce is refuted as not tautologous.
Category: Set Theory and Logic

[3] viXra:1803.0180 [pdf] replaced on 2018-03-13 17:40:00

Refutation of the Euathlus Paradox: Neither Pay © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 2 Pages. © Copyright 2018 by Colin James III All rights reserved.

Regardless of who wins the lawsuit of Portagoras, Euathlus does not pay. Hence the Euathlus paradox is refuted and resolved by default in favor of Euathlus.
Category: Set Theory and Logic

[2] viXra:1803.0094 [pdf] replaced on 2018-03-07 17:10:19

Refutation of Cantor's Original Continuum Hypothesis Via Injection and Binary Trees © Copyright 2018 by Colin James III All Rights Reserved.

Authors: Colin James III
Comments: 1 Page. © Copyright 2018 by Colin James III All rights reserved.

This is the briefest known such refutation of Cantor's continuum conjecture.
Category: Set Theory and Logic

[1] viXra:1803.0088 [pdf] submitted on 2018-03-07 03:33:06

The Continuum Hypothesis

Authors: Chris Pindsle
Comments: 12 Pages.

A proof of the Continuum Hypothesis as originally posed by Georg Cantor in 1878; that an uncountable set of real numbers has the same cardinality as the set of all real numbers. Any set of real numbers can be encoded by the infinite paths of a binary tree. If the binary tree has an uncountable node it must have a descendant with 2 uncountable successors. Each of those will have descendants with 2 uncountable successors, recursively. As a result the infinite paths of an uncountable binary tree will have the same cardinality as the set of all real numbers, as will the uncountable set of real numbers encoded by the tree.
Category: Set Theory and Logic