[4] **viXra:1704.0363 [pdf]**
*replaced on 2017-05-12 02:48:50*

**Authors:** Haroun Boutamani

**Comments:** 7 Pages.

This paper addresses the concept of selectivity using a main set and an auxiliary set, the auxiliary serves the purpose of deciding which elements do or do not fit together within the output sets chosen based on the elements of the main set.
This paper also presents an approach of comparing sets based on a defined relation, the sets’ properties, and the elementary properties being total compatibility and total incompatibility.
The problem classes P and NP are two sets considered under the criteria of distinguishability, then the possibility of comparison of the two sets is discussed. The proposed comparison presents a distinction between P and NP.

**Category:** Set Theory and Logic

[3] **viXra:1704.0161 [pdf]**
*submitted on 2017-04-13 03:51:02*

**Authors:** Ken Seton

**Comments:** 6 Pages. Enjoy

In the world of transfinite cardinality, any talk of number density, dart-board hits, proportions or probability is just a pouring from the empty into the void. Transfinite cardinality is unrelated to any normal concept of proportion or density over an interval and no understanding of it can obtained from probabilistic analogies. This is demonstrated by comparing extremely sparse and extremely dense collections of reals which are normally understood as uncountable and countable respectively. Should this incline one to think that Cantor’s equivalence definition is inappropriate for identifying the “size” of an infinite collection ?

**Category:** Set Theory and Logic

[2] **viXra:1704.0115 [pdf]**
*replaced on 2017-05-16 21:36:12*

**Authors:** Ken Seton

**Comments:** 9 Pages. Enjoy

Many have suggested that the infinite set has a fundamental problem. The usual complaint rails against the actually infinite which (say critics of various finitist persuasions) unjustifiably goes beyond the finite. Here we identify the exact opposite. The problem of the infinite set defined to have an identity (content) that is specified and restricted to be forever finite .
Set theory is taken at its word. The existence of the infinite set and the representation of irrational reals as infinite sets of terms is accepted. In this context, it is shown that the standard definition of the infinite countable set is inconsistent with the existence of its own classic convergents of construction. If the set is infinite then it must be quite unlike that which set theory asserts it to be.
Set theory found itself in some trouble over a century ago trusting an unrestricted anthropic comprehension. But serious doubt is cast on the validity of infinite sets which have been defined by a comprehension which overly-restricts their content.

**Category:** Set Theory and Logic

[1] **viXra:1704.0008 [pdf]**
*submitted on 2017-04-01 18:47:38*

**Authors:** Igor Hrncic

**Comments:** 2 Pages.

This letter is the short continuation of the previous paper titled "The infinitesimal error", available for free at the internet address http://vixra.org/abs/1703.0280. This letter is written just to further clarify the subject of "The infinitesimal error".

**Category:** Set Theory and Logic