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Virgil
Posts:
8,833
Registered:
1/6/11


Re: Infinity: The Story So Far
Posted:
Mar 7, 2014 4:01 PM


In article <24bf2be6c5e94ca8aa46b0cf85c43948@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> A proof is necessary for Peano's axioms because "successor" does not mean > "different successor", it does not even mean number. > >
Is WM claiming that the Peano axioms to not require a successor to be different from that of which it is a successor?
Or require that successors of different members are not themselves different?
Then WM's version of those Peano axioms must then be quite different from any standard English versions which explicitely require both.
And it is the Peano axioms that justify induction, and merely require, in addition, a couple of simple definitions to produce the natural numbers with their standard arithmetic.
That WM apparently cannot see this is a measure of how piss poor his mathematical vision is, 



