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Topic: Formal proof of the ambiguity of 0^0
Replies: 163   Last Post: Nov 13, 2013 10:45 AM

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Formal proof of the ambiguity of 0^0
Posted: Nov 3, 2013 5:37 PM

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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> > > 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

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

Thank you, Ross Finlayson

Date Subject Author
10/16/13 Dan Christensen
10/16/13 Brian Q. Hutchings
11/1/13 ross.finlayson@gmail.com
10/17/13 Robin Chapman
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 fom
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Peter Percival
10/17/13 Dan Christensen
10/17/13 Dan Christensen
11/2/13 Brian Q. Hutchings
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/18/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Ben Bacarisse
10/17/13 Dan Christensen
10/17/13 Robin Chapman
10/17/13 Dan Christensen
10/17/13 Bart Goddard
10/17/13 Dan Christensen
10/17/13 Brian Q. Hutchings
10/17/13 Brian Q. Hutchings
10/18/13 Robin Chapman
10/18/13 Dan Christensen
10/23/13 Shmuel (Seymour J.) Metz
10/25/13 Bart Goddard
10/29/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Robin Chapman
10/30/13 Bart Goddard
10/30/13 Peter Percival
10/30/13 Richard Tobin
10/30/13 fom
10/31/13 David Bernier
10/31/13 David Bernier
10/30/13 Dan Christensen
10/30/13 Bart Goddard
10/30/13 Dan Christensen
10/31/13 Bart Goddard
10/31/13 Dan Christensen
10/31/13 Bart Goddard
10/31/13 Dan Christensen
10/31/13 Bart Goddard
10/30/13 Peter Percival
10/30/13 JT
10/30/13 Dan Christensen
10/30/13 Peter Percival
10/30/13 Dan Christensen
10/30/13 Brian Q. Hutchings
10/30/13 Brian Q. Hutchings
10/30/13 JT
10/30/13 Peter Percival
10/30/13 JT
10/30/13 JT
10/30/13 Brian Q. Hutchings
10/18/13 Robin Chapman
10/18/13 Dan Christensen
10/18/13 fom
10/18/13 Dan Christensen
10/18/13 fom
10/18/13 Dan Christensen
10/18/13 Peter Percival
10/18/13 Dan Christensen
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Michael F. Stemper
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/23/13 Brian Q. Hutchings
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/20/13 Bart Goddard
10/20/13 Dan Christensen
10/21/13 Bart Goddard
10/21/13 Dan Christensen
10/21/13 Peter Percival
10/21/13 Bart Goddard
10/21/13 Dan Christensen
10/21/13 Bart Goddard
10/21/13 Peter Percival
10/21/13 fom
10/21/13 Bart Goddard
10/21/13 JT
10/21/13 Dan Christensen
10/21/13 JT
10/21/13 Dan Christensen
10/20/13 Peter Percival
10/20/13 Dan Christensen
10/23/13 Dan Christensen
10/23/13 fom
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 fom
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 Brian Q. Hutchings
11/1/13 Dan Christensen
11/1/13 Brian Q. Hutchings
11/2/13 Robin Chapman
11/1/13 Dan Christensen
11/1/13 Bart Goddard
11/1/13 ross.finlayson@gmail.com
11/3/13 ross.finlayson@gmail.com
11/3/13 Brian Q. Hutchings
11/1/13 Dan Christensen
11/2/13 Bart Goddard
11/2/13 Dan Christensen
11/2/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/12/13 Bart Goddard
11/13/13 Bart Goddard
11/13/13 Bart Goddard
11/2/13 Virgil
11/2/13 Dan Christensen
11/2/13 Bart Goddard
11/2/13 Paul
11/3/13 Bart Goddard
11/2/13 Dan Christensen
11/2/13 Dan Christensen
11/2/13 Ki Song
11/2/13 Virgil
11/2/13 Michael F. Stemper
11/2/13 Virgil
11/3/13 Michael F. Stemper
11/3/13 Robin Chapman
11/3/13 fom
11/3/13 Jussi Piitulainen
11/3/13 fom
11/4/13 Jussi Piitulainen
11/3/13 JT
11/3/13 JT
11/12/13 Dan Christensen
11/13/13 Dan Christensen