Einstein's Diffusion and Probability-Wave Equations of Random ...

Gauge Institute Journal,
H. Vic Dannon
1.
Hyper-real Line
The minimal domain and range, needed for the definition
and analysis of a hyper-real function, is the hyper-real line.
Each real number α can be represented by a Cauchy
sequence of rational numbers, ( r , r , r ,...) so that r → α .
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The constant sequence ( ααα , , ,...) is a constant hyper-real.
In [Dan2] we established that,
1. Any totally ordered set of positive, monotonically
n
decreasing to zero sequences
family of infinitesimal hyper-reals.
( ι1, ι2, ι3,...)
constitutes a
2. The infinitesimals are smaller than any real number,
yet strictly greater than zero.
1 1 1
3. Their reciprocals ( , , ,...
ι 1
ι 2
ι 3
) are the infinite hyperreals.
4. The infinite hyper-reals are greater than any real
number, yet strictly smaller than infinity.
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