The number x^x increases or decreases?
V.Gopal
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?
David C. Ullrich
wrote:
>We always imagine 'x' to be a variable
Yup. Like we always imagine George Bush to be the president of the
United States.
>and we never imagine what
>happens to x when "it" increases continuously.
We don't? Some of us do, fairly often.
>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 decreases for 0 < x < 1/e and then increases for x > 1/e.
David C. Ullrich
Ms O. Philia
> We always imagine 'x' to be a variable
Good point. Let's imagine 'x' to be something unimaginable instead.
;-)
>and we never imagine what happens to x when "it" increases continuously.
Or we could go one step further and imagine x's increase is
accelerating.
>To exclude human control on 'x' let us imagine that x is time-like and it
begins to
> increase continuously from 0.
Kind of like the big bang.
>Obvioisly 'x' is positive. Now what happens to x^x as 'x' increases from
0?
That would depend on how we defined x^x. For example, it might be taken
to signify a parallel universe of opposite entropy in which a being named
lapoG .V had all the same ideas as you only backwards. Thus, to answer your
title question, the increase or decrease of x^x results from which way the
arrow of time points.
Mitchell Smith
"Ms O. Philia" wrote:
And, you are aware, of course, that information theory has a notion of entropy
which is called negentropy in order to differentiate it from the thermodynamic
notion?
Of course, we have an ontological commitment to which is physical and which is
in our minds...
:-)
mitch
Nobuo Saito
>
> >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 decreases for 0 < x < 1/e and then increases for x > 1/e.
>
> David C. Ullrich
Forgive me to explain this in detail.
Let y = x^x.
log y = x log x. Hence y = exp(x log x). Hence dy/dx = (1 + log x)y.
Since y > 0, dy/dx < 0 when 0 < x < 1/e and dy/dx > 0 when x > 1/e.
Nobuo Saito
Douglas Eagleson
"V.Gopal" wrote:
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
William Elliot
That's an excessive amount of human control you put upon x with your
imagination, that x is real nothing, but it won't stay that way.
You also put large amount of human control upon time with your same
overactive imagination that regiments zero chronos quanta.
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William Elliot
> Yup. Like we always imagine George Bush to be the president of the
> United States.
>
Hm, another prosetic application of complex immaginaries other that
Author Anderson/Enron accounting.