Ahocsb.108
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utcsrgv!utzoo!decvax!duke!chico!harpo!npois!houxi!hocsb!bsm
Wed Mar 3 10:44:35 1982
Reply To FUNCTIONAL INFINITY
Several years ago (nowhere near infinity) I was discussing a similar
idea with a friend. We never thought to consider the vector
implications, thus our idea diverged somewhat from yours.
This infinity was a general range of values (or distances)
that could not be represented by our usual numerical system.
It might be visualized as moving the decimal point to the
left by some reference distance (10 ** 1000), the result
being that all usual numbers now (almost) equal zero and
all the infinity numbers are now scaled down to the usual
numbers. This visualization is poor because these numbers
of infinity can still be represented by the usual number
system.
It would be a significant step if someone could
develop a math system for dealing with such numbers. I
beleive this has already been done by Isaac Newton around
1675 and possibly Archimedes before Christ. Calculus
always deals with numbers that are to small to be represented
by the usual numerical system, these numbers being called
DELTA's. In many Calculus derivations, reciprocals of
Delta's arise and must be eliminated by inversion.
These reciprocals of Delta's are FUNCTIONAL INFINITIES.
Unfortunately, the Calculus always eliminates them to
obtain a result. What is needed is a way of directly
dealing with them, or treating them as "ANTI-DELTA's".
(This would be distinct from Antiderivative or Integral)
L'Hopital's Rule is a nice start, but it only evaluates
points on a function, and what we need are functions
whose values are infinite everywhere.
I enjoyed your vector description of infinity, but
I disagree on a major concept. If the infinite position was
at a distance relatively infinite from all other positions.
, then there would be only one direction. This would be
from the infinite position toward all the other positions.
Although this puts a kink in some of your observations, it
could have some astounding uses. By introducing infinity to
a 3 dimensional system, it reduces the system to one dimension.
......but maybe this observation is incorrect......?
I would appreciate any re-replies or additional
information. Sorry for being so wordy.
yours till the end of time,
Bryan Moffitt
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