
Re: Can addition be defined in terms of multiplication?
Posted:
Aug 20, 2013 5:18 AM


> Actually, more is known. Neither addition nor multiplication is > > definable from successor alone;
This is all it takes to do addition:
PROGRAM LIST 1 + X 0 X 2 + X [ s Y ] [ s Z ] < + X Y Z
TRACE + [s[s 0]] [s 0] ANS ?
HEAD 1 + X [ s Y ] [ s Z ] [AXIOM 2] TAIL 1 + X Y Z + [ s s 0 ] [ 0 ] Z HEAD 1 + X 0 X [AXIOM 1] MATCH TRUE 1 MATCH
+ [s[s 0]] [s 0] ANS ?
ANS = s s s 0
Try it for yourself if you don't believe me!
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