"V.Gopal" wrote:
> We always imagine 'x' to be a variable and we never imagine what
> happens to x when "it" increases continuously. To exclude human
> control on 'x' let us imagine that x is time-like and it begins to
> increase continuously from 0. Obvioisly 'x' is positive. Now what
> happens to x^x as 'x' increases from 0?
It will display the property of the mathematics applied to the relation
x^x. When less than zero it does that stuff. And when less than
a unit, it will does the same stuff as the mathematics
that allows negative numbers in the abstract.
The convention of calling the complex algebra a necessary
number system is part of contemporary stuff mathematics.
Your question asks the reader to think of the abstract number
between 0 and 1, and to explain the relation's necessary
behavior. The behavior there in relation to the above 1, x behavior,
is distinctly unique.
And the answer of what happens in the abstract numersoity
is a dislocation of the transformation of a number to another
number. Normally a number may transfrom another to
state the transformation. For example a multiplication
transforms.
And the number less than one should be likewise transformable
without effect on the relation's relative rate in the abstract.
A decimal less than one appears distinct from all those greater than one
to
very far away. Pick a one in relation to a large number and the
the difference is always positive.
Pick a decimal in relation to another less than one and the
slope is always negative.
So, the derivative of the function appears as the distinct
behavior difference.
And to resolve the meaning of the necessity for the form of the
differential in common mathematics is considered
to hard to bother with. To date the stuff mathematics
has not stated a theory of the differential.
A statement that a method of differential solution appears
true, without reference to the cause of the solution's form
is the contemporary theory of the differential.
In reality anything goes in differential theory. I look to
a constant of another theory as the necessity of the
differential's existence. And then transcendental
necessity appears as the cause of the differential's
form. A form of the theory of the atom applied
as the physical constant.
Atoms are funny things being for example, the abstract Pi
of the particular circle's pi. And then everybody
tries to figure out why there is a transcendental Pi,
ouch my head hurts.
And all that is necessary is to study Greek Mathematics.
Except the translations stink. Go stare at those two
sticks for a few weeks, much more fun than Pi thinking.
Douglas Eagleson
Gaithersburg, MD USA
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