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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: 4,417 Registered: 5/20/10
Re: Can addition be defined in terms of multiplication?
Posted: Aug 18, 2013 6:12 PM
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On Friday, August 16, 2013 1:54:40 AM UTC-7, Peter Percival wrote:
> Can addition be defined in terms of multiplication? I.e., is there a
>
> formula in the language of arithmetic
>
>
>
> x + y = z <-> ...
>
>

Yes but you just get an equivalent formula for standard peano addition.

X + 0 = X
X + s(Y) = s(Z)

---------------

This works in www.phpPROLOG.com

n^(X) is just a Prefix Function symbol like f(x)

PROGRAM LIST

1 + [ n^ X ] [ n^ 0 ] [ n^ X ]

2 + [ n^ X ] [ n^ [ s Y ] ] [ n^ [ s Z ] ] :-
+ [ n^ X ] [ n^ Y ] [ n^ Z ]

3 + X Y Z :-
+ [ n^ X ] [ n^ Y ] [ n^ Z ]

TRACE
+ [s 0] [s[s 0]] ANS ?

HEAD 1
+ X Y Z
TAIL 1
+ n^ X n^ Y n^ Z
+ n^ [ s 0 ] n^ [ s s 0 ] n^ Z
HEAD 1
+ [ n^ X ] [ n^ [ s Y ] ] [ n^ [ s Z ] ]
TAIL 1
+ n^ X n^ Y n^ Z
+ n^ [ s 0 ] n^ [ s 0 ] n^ Z
HEAD 1
+ [ n^ X ] [ n^ [ s Y ] ] [ n^ [ s Z ] ]
TAIL 1
+ n^ X n^ Y n^ Z
+ n^ [ s 0 ] n^ [ 0 ] n^ Z
HEAD 1
+ [ n^ X ] [ n^ 0 ] [ n^ X ]
MATCH
TRUE 1
MATCH
TRUE 1
MATCH
TRUE 1
MATCH

+ [s 0] [s[s 0]] ANS ?

ANS = s s s 0

Herc
--
www.phpPROLOG.com

www.tinyurl.com/HOW-PROLOG-WORKS

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

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