[this document requires HTML-superscript-ing]

[under construction - preliminary draft needs typography]

We take the infinitesmally closed interval in deference to finitesmality, and to a possibly finer ruler.

Let a, a+1, ... be numbers adjacent by smallest measurable quanta=1,
one finitesmal; and let x: a+1>x>a be a measurable value on the same domain.
If (and we're looking for the contradiction to if) x leans
distinguishably more toward a than toward a+1, which we denote,
a+1 ^{m}> x, meaning x measures less than a+1,
then in fact we could have resolved further the distinguishable
adjacency of a, a+1,..., and we may presume then we already did so
[in eliminating the contradiction] - to wit:
if x : a+1 m> xo > y > a (validly: a+1 > xo) then xo, 2a+1-xo
subdividee the interval (a,a+1) into three distinguishable pieces:
lesser quanta, around and between a,a+1, that is, around a,a+.5,a+1,
where "a+.5" is short notation for, between a,a+1.
Obviously a contradiction: x measured cannot be more accurate/precise
than the ruler, else we'd have merely defined a way of obtaining a+.5:
after finishing that definition at a,a+1,....
This may change our skill at taking measurements, by observing around-ness
and between-ness; but it cannot improve on the best possible measure of x,
and therefor neither a+1>x nor x>a - x is not distinguishably toward,
around, nor between a,a+1.

Whence x is indistinguishable on [x-1,x+1], while it is distinguishable
outside. Thus the a's themselves are vestigially indistinguishable, as adjacent,
while distinguishable further away than immediate.
Just possibly a ^{m}= a+1.

- [We take the infinitesmally closed interval in deference to
finitesmally, and to possibly finer ruler]

Any x then, must measure indistinguishably as either of the nearest two a's,
or in the extreme case of x=a, as among {a-1,a,a+1}.
[Possibly x^{m}=x-1,x+1]

[x : ... , is read, "x for/ [be] such-that/where [it[is]] ..." . . . . . .

However, the precise nature of the semi-natural normal distributed uniform finite covering is such that, although the representative selection of an exact sample as itself, is just 50%, the misselection by some near-representation (of an exact sample) is minutely greater at 0.500006975 - a curiosity that infinite sums of equally spaced consecutive normal distributions converge rapidly to uniform on the whole, for smaller meshes, but not identically: the half-way between numbers are representatively selected slightly less than 100% (for all possible) and thereby compensates mostly. To characterize this more reasonably, the normal distribution is not perfectly ideal. *

* [sampling on some uniform detectors yields a triangular distribution]

Thus by notion our ruler line is graduated with near-triangular half-height distributions overlapping on half-widths (still each a full unit-for-unit likelihood, but spread over two), whereín each exactly half-way number is representatively selected as (equally) either nearest neighbor, 82% total occasionally or 41% each nearest neighbor (better than strictly triangular 75%, or 37.5% each). . . . .

'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