Date: Nov 3, 2013 5:37 PM Author: ross.finlayson@gmail.com Subject: Re: Formal proof of the ambiguity of 0^0 On Friday, November 1, 2013 8:33:26 PM UTC-7, Ross A. Finlayson wrote:

> On Friday, November 1, 2013 8:29:52 PM UTC-7, Bart Goddard wrote:

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> > Dan Christensen <Dan_Christensen@sympatico.ca> wrote in

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> > news:63ae3975-e4f7-4381-9df0-4957c8b0f5e9@googlegroups.com:

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> > > As I have said repeatedly, it is assumed to be a natural number, but

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> > > no specific value is assigned to it. So, yes, that makes it

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> > > "undefined." What is your point, Barty?

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> > The point, as I've said repeatedly, is that your

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> > "theorem" assumes that it has a value. If it's not

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> > defined, then it has no value (or meaning.) Contradiction.

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> > 0^1 is defined in terms of 0^0. So now, 0^1 is

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> > undefined. 0^2 is defined in terms of 0^1, so

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> > 0^2 is now undefined. Etc. So, by induction,

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> > you haven't defined 0^(anything). We, in the business,

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> > call this "logic."

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> Leave together the parts that work.

What do you mean zero to "the" zero?

I see it's written write there the zero and the other zero

right there above it. Zero to the zero or zero, zero to

the zeroeth power, anything to the zeroeth power equals 1.

Zero, though, otherwise for anything else, zero to any

power is zero. Besides zero, zero, any number of products

of copies of zero is zero. Yet, sometimes: zero to the

zeroeth power is better evaluated as one, here as it is

the discontinuity for that for everything else X, X^0 = 1.

Here the point is there are two zeroes, zero the scalar

and zero the exponent. If being about 1 is an ideal

condition, then it is one.

Then in the frameworks like the theory where there are

counterexamples, that's basically established on the

contingency that all the numbers here simply and well

enough about the zeroes, are as to expected continuity of

their conditions.

Well now I'm sure I have my ignorance here enough for

that, yet, I find Peter and Dan should work to accommodate

that intuitively and constructively each has its points,

as to axiomatics, those being domain axiomatics or model.

Those are then stipulations on the notation as to their

general context and simply making clear or pointing out

the discrepancy for each.

Then about effects where for those two functions they're

each other's discontinuities, it makes there as zero is

central for the general usual case where zero is central

or original.

x^0 = 1

0^x = 0

These are relevant as generally the parameter estimation

sees each as relevant or not contrary to approximation, as

they are used with approximating terms in relative

(linear) frameworks for the behavior as the value goes to

zero, or through zero.

The functions or identities are state without otherwise

assumptions as to x which here is the point of discrepancy

as to how the other would apply, these identities as

functions (i.e., here constants or identities and the

identity establish enough their nullity in their

frameworks about them).

It seems that if you set x^0 or 0^x it would have the

constant value.

Thank you, Ross Finlayson