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Topic: Can addition be defined in terms of multiplication?
Replies: 58   Last Post: Aug 23, 2013 3:56 PM

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 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: Can addition be defined in terms of multiplication?
Posted: Aug 19, 2013 9:07 PM

On Sunday, August 18, 2013 3:40:08 PM UTC-7, graham...@gmail.com wrote:
> > 2 x [ n^ X ] [ n^ [ s Y ] ] [ n^ [ s Z ] ] :-
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> >
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> >
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> >
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> > + [ n^ X ] [ n^ Y ] [ n^ Z ]
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> TYPO:
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> x [ n^ X ] [ n^ [ s Y ] ] [ n^ [ s Z ] ] :-
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> x [ n^ X ] [ n^ Y ] [ n^ Z ]
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> this is:
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> 2^x * 2^(y+1) = 2^(z+1)
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> <-
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> 2^x * 2^y = 2^z
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> which is just an adaption of Peano Addition / same algorithm.
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> x + y+1 = z+1
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> <-
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> x + y = z
>

This still uses SUCCESSOR

2^x * 2^(y+1) = 2^(z+1)
<-
2^x * 2^y = 2^z

The only way to avoid that (if you consider successor addition)

would be a different number structure.

1 = 2^0 = 1
2 = 2^1 = t(1)
4 = 2^2 = t(t(1))
8 = 2^3 = t(t(t(1)))
...

might be able to handle composite + composite = composite

1 + 2 = X
2^1 * 2^2 = 2^X
X = |t(1)| + |t(t(1))|

but I have other things to work on....

Herc
--
www.phpPROLOG.com

Date Subject Author
8/16/13 Peter Percival
8/16/13 William Elliot
8/16/13 Peter Percival
8/16/13 David C. Ullrich
8/16/13 namducnguyen
8/17/13 Peter Percival
8/17/13 namducnguyen
8/17/13 fom
8/23/13 tommy1729_
8/16/13 Peter Percival
8/16/13 Robin Chapman
8/16/13 Helmut Richter
8/16/13 Rotwang
8/16/13 Virgil
8/22/13 Rock Brentwood
8/16/13 Shmuel (Seymour J.) Metz
8/17/13 Helmut Richter
8/16/13 Jim Burns
8/16/13 fom
8/17/13 Robin Chapman
8/17/13 fom
8/17/13 Peter Percival
8/17/13 fom
8/17/13 Peter Percival
8/17/13 Peter Percival
8/18/13 William Elliot
8/18/13 Peter Percival
8/18/13 William Elliot
8/18/13 Peter Percival
8/18/13 Graham Cooper
8/18/13 David C. Ullrich
8/18/13 David C. Ullrich
8/17/13 Graham Cooper
8/18/13 David Bernier
8/18/13 Ben Bacarisse
8/18/13 Peter Percival
8/18/13 Jim Burns
8/18/13 fom
8/18/13 Ben Bacarisse
8/18/13 Graham Cooper
8/18/13 Graham Cooper
8/18/13 Graham Cooper
8/18/13 Graham Cooper
8/19/13 Graham Cooper
8/19/13 Alan Smaill
8/19/13 fom
8/19/13 Alan Smaill
8/20/13 Alan Smaill
8/20/13 Peter Percival
8/20/13 Graham Cooper
8/20/13 Graham Cooper
8/22/13 David Libert
8/22/13 Peter Percival
8/20/13 fom