[this document requires HTML-superscript-ing]

[under construction]

"Therefore, there exist numbers in the list, in-finitesmally close to SQRT 2 (the Rationals near SQRT 2) however indeterminably"

* [The author uses an Hewlett Packard HP21S STAT/MATH electronic programmable calculator for tabular excerptations]

Included as appendices are, prerequisite discussion: a consumus of arithmetic methods for the student-computor, a matriculus (though I am ever inclined to call this, gut arithmetic, for its iteratively simple linear systematic transformation processes and products), and a calculus done in the here-preferred style of infinitesmals - all useful predicates to the purposes, designs, and application-opportunities of the general purpose digital computer, as it was once known industrially.

And we begin by meeting a challenge intimated and forworded preceding, inasmuch as to extricate ourselves from a certain blythe tendency among early pupils of the mathematica to accede to proof-by-intimidation.

* or conversely, if 1.000... were outside, then 0.999... is already excluded

Of course, in finite-smal measure, 0.999...=1.000..., because there is no measurably finite difference; But equality in general, no: Since adjacent numbers with equally many digits divide the interval equally [0.0,0.1,...0.9,1.0] divides the interval [0,1] equally, in equal intervals of 0.1, (then) when all digits are specific (hypothetically possible, but not within our finite canon), then, {0.000...,...,0.999...,1.000...} must be the endpoints of [0.1] plus all the equally spaced dividers of the same interval: And then, if 0.999... equals 1.000... so that its subinterval 0.000... is identically 0, zero, all would equal 1.000..., as all the subintervals were so identically zero, and (intuitively) the integral summation of identically zero, is zero. Here we see the final break in the generalization of equality: We tacitly assume that the sum (the infinite sum) of all the subintervals must equal the whole interval [0,1], but infinity times zero, is zero: only infinity times infinite-smal, may accumulate to some finite (or other arbitrary value), and thereby we have distinguished infinitesmals as real quantities - as irrational as that first seemed. In short, we must be especially aware of our meaning of equality: For this reason we include calculus by infinitesmals. *

* [space-time physicists aren't alone who integrate zero to nonzero]

Computus (on the other hand) is by definition a finite covering; And we begin with our notion of equality. The argument preceding is not lost in the computus, but gives it a special flavor: As we shall see immediately, adjacent numbers in precise measure are vestigially indistiguishable: a new tenor of equality. But, in the finite cleavage of computus it takes only a step across (an) adjacent number(s) to reach distinguishability. Then also we must develop the notions of inequality and inclusion: numbers with their own precision lie constrainted upon specifiable activity domains (or even within bounds). Taking one last overview so as to not escape our imminent entry in the computus, we foresee our first concern for significant digits, shall also be our last concern: Our new concept of number must carry with it a sense of precision adaptable to grand accumulations and iterations; We will revise all estimates and notions until we have a stable base concept; and our finished product must be a simple as when we began in the earliest grades of school to learn the arithmetic of decimal places and natural numbers, then operations advanced beyond counting.

'Majestic Service in a Solar System'

Nuclear Emergency Management

The theory of measurement propounded in this work is not to be cited (as) considering contraband or corpses; Nor are the intellectual appurtenances herein to be used for or in the commission of crimes against persons, peoples, properties, or powers (states). May your tabernacle measure true.

COPYRIGHT: BASIC LIBRARY RULES: NONTRANSFERABLE: READ QUIETLY

- CHARGES FOR OTHER USES:
- $1 per copy, reproduction, translation, implementation,

or systematic, paraphrase, depiction, evaluation, comparison; - plus additional media costs, less efficiency discounts;
- unauthorized use, treble standard;
- final charges greater or lesser per U.S.A. Copyright Law,

regarding fair-use/citation and second-source/mirror-site.

Mr. Raymond Kenneth Petry