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Topic: 0^0=1
Replies: 145   Last Post: Jun 5, 2012 1:10 PM

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David W. Cantrell

Posts: 3,395
Registered: 12/3/04
Re: 0^0=1
Posted: May 8, 2012 10:42 AM
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PotatoSauce <kiwisquash@gmail.com> wrote:
> On Monday, May 7, 2012 6:05:38 PM UTC-4, Ross wrote:
<snip>
> > The second is noting that:
> >
> > x^4 = x * x * x * x
> > x^3 = x * x * x
> > x^2 = x * x
> > x^1 = x
> > x^0 = ?

>
> How about
>
> x^4 = 1*1 * x * x * x * x
> x^3 = 1*1 * x * x * x
> x^2 = 1*1 * x * x
> x^1 = 1*1 * x
> x^0 = 1*1
>
> I put two "1"s instead of just 1, in case you feel like multiplication
> can only be done when there are at least two numbers.


I had thought of posting essentially the same thing, together with an
explanation:

Algebra students know that a term's numerical coefficient, when not
otherwise specified, is _understood_ to be 1. But let's _explicitly_ show
that numerical coefficient on the right side of the equations in the
pattern that Ross gave.

x^4 = 1 * x * x * x * x
x^3 = 1 * x * x * x
x^2 = 1 * x * x
x^1 = 1 * x
x^0 = 1

Here's what's going on. In _any_ multiplication, there is a factor of 1 "in
the background", so to speak. Of course, since 1 is the multiplicative
identity, having it in the background is perfectly innocuous. And if our
product is in "simplified form", that 1 in the background will _never_ be
seen _unless there is no other factor of any sort_.

In the pattern above, going from the top line down, we erase a factor of x
on the right each time until, when no factors of x remain, the background 1
is finally revealed!

David W. Cantrell


Date Subject Author
4/20/12
Read 0^0=1
Don H
4/20/12
Read Re: 0^0=1
Virgil
4/20/12
Read Re: 0^0=1
Pubkeybreaker
4/20/12
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J. Antonio Perez M.
4/20/12
Read Re: 0^0=1
Richard Tobin
4/20/12
Read Re: 0^0=1
Don H
4/21/12
Read Re: 0^0=1
LudovicoVan
4/21/12
Read Re: 0^0=1
Peter Webb
4/21/12
Read Re: 0^0=1
Dave Dodson
4/21/12
Read Re: 0^0=1
Peter Webb
4/21/12
Read Re: 0^0=1
Don H
4/21/12
Read Re: 0^0=1
Frederick Williams
4/21/12
Read Re: 0^0=1
Don H
4/21/12
Read Re: 0^0=1
Frederick Williams
4/21/12
Read Re: 0^0=1
Bart Goddard
4/22/12
Read Re: 0^0=1
Don H
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/22/12
Read Re: 0^0=1
Bart Goddard
4/22/12
Read Re: 0^0=1
Virgil
4/23/12
Read Re: 0^0=1
Frederick Williams
4/23/12
Read Re: 0^0=1
Pubkeybreaker
4/23/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Dave Dodson
4/22/12
Read Re: 0^0=1
Pubkeybreaker
4/22/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Pubkeybreaker
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/22/12
Read Re: 0^0=1
Peter Webb
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/23/12
Read Re: 0^0=1
Pubkeybreaker
4/22/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Frederick Williams
5/7/12
Read Re: 0^0=1
Ross Clement
5/7/12
Read Re: 0^0=1
LudovicoVan
5/7/12
Read Re: 0^0=1
exmathematician
5/7/12
Read Re: 0^0=1
Ki Song
5/7/12
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LudovicoVan
5/7/12
Read Re: 0^0=1
Ki Song
5/7/12
Read Re: 0^0=1
LudovicoVan
5/7/12
Read Re: 0^0=1
Ki Song
5/10/12
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Michael Stemper
5/7/12
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Frederick Williams
5/7/12
Read Re: 0^0=1
LudovicoVan
5/8/12
Read Re: 0^0=1
Butch Malahide
5/8/12
Read Re: 0^0=1
LudovicoVan
5/8/12
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Ross Clement
5/8/12
Read Re: 0^0=1
Jussi Piitulainen
5/7/12
Read Re: 0^0=1
Ross Clement
5/8/12
Read Re: 0^0=1
Frederick Williams
5/8/12
Read Re: 0^0=1
Ki Song
5/8/12
Read Re: 0^0=1
David W. Cantrell
5/8/12
Read Re: 0^0=1
Dan Christensen
5/8/12
Read Re: 0^0=1
Frederick Williams
5/8/12
Read Re: 0^0=1
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5/8/12
Read Re: 0^0=1
William Hale
5/8/12
Read Re: 0^0=1
Dan Christensen
5/9/12
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Frederick Williams
5/10/12
Read Re: 0^0=1
Michael Stemper
5/10/12
Read Re: 0^0=1
Dan Christensen
5/9/12
Read Re: 0^0=1
Frederick Williams
5/9/12
Read Re: 0^0=1
Dan Christensen
5/9/12
Read Re: 0^0=1
LudovicoVan
5/10/12
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Michael Stemper
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Read Re: 0^0=1
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5/8/12
Read Re: 0^0=1
Frederick Williams
5/22/12
Read Re: 0^0=1
Michael Press
5/28/12
Read Re: 0^0=1
address_is@invalid.invalid
5/28/12
Read Re: 0^0=1
address_is@invalid.invalid
6/5/12
Read Re: 0^0=1
Michael Press
4/21/12
Read Re: 0^0=1
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4/21/12
Read Re: 0^0=1
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4/23/12
Read Re: 0^0=1
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4/25/12
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4/21/12
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LudovicoVan
4/21/12
Read Re: 0^0=1
Richard Tobin
4/21/12
Read Re: 0^0=1
Efftard K. Donglemeier
4/22/12
Read Re: 0^0=1
Frederick Williams
4/22/12
Read Re: 0^0=1
Don H
4/22/12
Read Re: 0^0=1
Bart Goddard
4/23/12
Read Re: 0^0=1
harold james
4/23/12
Read Re: 0^0=1
Don H
4/24/12
Read Re: 0^0=1
Bart Goddard
4/24/12
Read Re: 0^0=1
Frederick Williams
4/24/12
Read Re: 0^0=1
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4/22/12
Read Re: 0^0=1
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4/22/12
Read Re: 0^0=1
Wally W.
4/22/12
Read Re: 0^0=1
J. Antonio Perez M.
4/22/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Jussi Piitulainen
4/23/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Jussi Piitulainen
4/23/12
Read Re: 0^0=1
Dan Christensen
4/23/12
Read Re: 0^0=1
Frederick Williams
4/23/12
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4/23/12
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Read Re: 0^0=1
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4/23/12
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4/24/12
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4/25/12
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4/25/12
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4/25/12
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4/25/12
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4/25/12
Read Re: 0^0=1
David W. Cantrell
4/25/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Jussi Piitulainen
4/26/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
Rotwang
4/26/12
Read Re: 0^0=1
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4/25/12
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Read Re: 0^0=1
Jussi Piitulainen
4/25/12
Read Re: 0^0=1
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4/26/12
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4/26/12
Read Re: 0^0=1
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4/26/12
Read Re: 0^0=1
Jussi Piitulainen
4/26/12
Read Re: 0^0=1
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4/27/12
Read Re: 0^0=1
Jussi Piitulainen
5/22/12
Read Re: 0^0=1
Michael Press
5/22/12
Read Re: 0^0=1
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5/23/12
Read Re: 0^0=1
Michael Press
4/23/12
Read Re: 0^0=1
Frederick Williams
4/27/12
Read Re: 0^0=1
Frederick Williams
4/26/12
Read Re: 0^0=1
Dan Christensen
4/26/12
Read Re: 0^0=1
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4/27/12
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4/27/12
Read Re: 0^0=1
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Repeating Rifle
4/27/12
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jbriggs444@gmail.com
4/28/12
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Repeating Rifle
4/28/12
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4/28/12
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4/27/12
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Shmuel (Seymour J.) Metz
4/29/12
Read Re: 0^0=1
Dr J R Stockton
4/29/12
Read Re: 0^0=1
David W. Cantrell

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