[3] **viXra:1011.0038 [pdf]**
*submitted on 17 Nov 2010*

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache

**Comments:** 249 pages

This Interval arithmetic or interval mathematics developed in
1950's and 1960's by mathematicians as an approach to putting
bounds on rounding errors and measurement error in
mathematical computations. However no proper interval
algebraic structures have been defined or studies. In this book
we for the first time introduce several types of interval linear
algebras and study them.

**Category:** Algebra

[2] **viXra:1011.0037 [pdf]**
*submitted on 14 Nov 2010*

**Authors:** Nathaniel S. K. Hellerstein

**Comments:** 17 pages

This paper redefines the addition of rational numbers, in a way that allows division
by zero. This requires defining a "compensator" on the integers, plus extending
least-common-multiple (LCM) to zero and negative numbers. "Compensated addition"
defines ordinary addition on all ratios, including the 'infinities' n/0, and also
'zeroids' 0/n. The infinities and the zeroids form two 'double ringlets'. The lattice
rationals modulo the zeroids yields the infinities plus the 'wheel numbers'. Due to
the presence of the 'alternator' @ = 0/-1, double-distribution does not apply, but
triple-distribution still does.

**Category:** Algebra

[1] **viXra:1011.0019 [pdf]**
*submitted on 11 Nov 2010*

**Authors:** Nathaniel S. K. Hellerstein

**Comments:** 33 pages

In this paper I discuss "reduction", a.k.a. "reciprocal addition"; addition conjugated by reciprocal.
I discuss reduction's definition, its laws, its graphs, its geometry, its algebra, its calculus, and its
practical applications. This paper contains a problem set with answer key.

**Category:** Algebra