
Re: A finite set of all naturals
Posted:
Aug 14, 2013 4:22 PM


In <UHhOt.266168$Ln4.151439@fx24.iad>, on 08/12/2013 at 09:26 PM, Nam Nguyen <namducnguyen@shaw.ca> said:
>The point is though the essences of the 2 conjectures are drastically >different: _an odd number can not be defined without addition_ while >an even number can (as per Def03b above).
Who uses an axiom system for naturals or integers that includes multiplication but not addition?
>And of course arithmetically, induction, from a binary operation >point of view, would not be possible without addition, designated as >'+'.
Induction only requires the unary "S", not the binary "+", although the latter is often convenient.
 Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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