[6] **viXra:1804.0351 [pdf]**
*submitted on 2018-04-25 09:48:21*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

The definition of multiplication for extended complex numbers and undefined values of ∞–∞ and 0×∞ are theorems.
The definition of addition for extended complex numbers is not a theorem.
The custom of forcing a field definition for extended complex numbers is mistaken as are the undefined values of the quotients 0/0 and ∞/∞.

**Category:** Set Theory and Logic

[5] **viXra:1804.0272 [pdf]**
*submitted on 2018-04-19 16:13:42*

**Authors:** Colin James III

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

The "Epicurean paradox" or "Riddle of Epicurus" is a version of the problem of evil.
As rendered it is tautologous.
This means that the paradox of Epicurus as invoked by Epictetus is refuted as a contradiction, and is confirmed as a theorem and not as a paradox.

**Category:** Set Theory and Logic

[4] **viXra:1804.0174 [pdf]**
*replaced on 2018-05-04 01:07:50*

**Authors:** Seamus McCelt

**Comments:** 2 Pages.

If you claim there are particles: there would actually have to be particles.

And that would mean there are about 18 different microscopic things that work flawlessly together -- just like clockwork to make even just one basic atom "gear" set.

If you have larger sized atoms: it would be like throwing more and more gear sets into the clockwork -- but that is ok because no matter what you throw in -- it will still work just fine.

How can an infinity of 18 different things (infinity times 18 different things) just happen to be here, know how work together as a group and also successfully work together as a group(s)?

How is that possible? It isn't...

Stuff cannot be made from what they call "particles."

If there are particles; this is equation of the universe:

Universe = Infinity × {a,b,c,d,f,g,h,j,k,l,m,o,p,q,t,w,x,y,z}

**Category:** Set Theory and Logic

[3] **viXra:1804.0142 [pdf]**
*submitted on 2018-04-10 00:18:01*

**Authors:** Colin James III

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

The axiom of Tarski-Grothendieck set theory is refuted as contradictory.

**Category:** Set Theory and Logic

[2] **viXra:1804.0136 [pdf]**
*submitted on 2018-04-10 07:22:27*

**Authors:** Colin James III

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

The axiom for Tarski–Grothendieck set theory as rendered in the Metamath proof explorer in axiom ax-garth is refuted as contradictory.
This raises serious questions about the logical accuracy and proof puissance of "Metamath".

**Category:** Set Theory and Logic

[1] **viXra:1804.0067 [pdf]**
*submitted on 2018-04-04 15:38:26*

**Authors:** Franco Sabino Stoianoff Lindstron

**Comments:** 22 Pages.

Any system of 'big' Boolean equations can be reduced to a single Boolean equation {í µí±”(í µí²) = 1}. We propose a novel method for producing a general parametric solution for such a Boolean equation without attempting to minimize the number of parameters used, but instead using independent parameters belonging to the two-valued Boolean algebra B2 for each asserted atom that appears in the discriminants of the function í µí±”(í µí²). We sacrifice minimality of parameters and algebraic expressions for ease, compactness and efficiency in listing all particular solutions. These solutions are given by additive formulas expressing a weighted sum of the asserted atoms of í µí±”(í µí²), with the weight of every atom (called its contribution) having a number of alternative possible values equal to the number of appearances of the atom in the discriminants of í µí±”(í µí²). This allows listing a huge number of particular solutions within a very small space and the possibility of constructing solutions of desirable features. The new method is demonstrated via three examples over the 'big' Boolean algebras, í µí°µ 4 , í µí°µ 16 , and í µí°µ 256 , respectively. The examples demonstrate a variety of pertinent issues such as complementation, algebra collapse, incremental solution, and handling of equations separately or jointly.

**Category:** Set Theory and Logic