Re: Turing completeness of the functional paradigm?

Mr Elliot:

> > > To get rational and real numbers from Peano's axioms you have to add set
> > > theory.
> >
> > I see (but I thought they were merely Peano sequences of Peano
> > sequences,
>
> For sequences you need set theory.
>
> > i.e. vectors of this or other sort, as is every mathematical object).
>
> Make no sense.

I see. As I said, I _most_ gladly surrender to your expertise.

Thank You very much for writing.
Tom

.

Relevant Pages

  • Re: Turing completeness of the functional paradigm?
    ... >> To get rational and real numbers from Peano's axioms you have to add set ... > I see (but I thought they were merely Peano sequences of Peano ... For sequences you need set theory. ...
    (sci.logic)
  • Re: Turing completeness of the functional paradigm?
    ... > To get rational and real numbers from Peano's axioms you have to add set ... I see (but I thought they were merely Peano sequences of Peano ... > It's a true statement about integers that can't be proved with Peano's ... Mr Elliot. ...
    (sci.logic)
  • Re: V
    ... (which could be indexed by all the *finite* sequences of natural ... numbers with a certain well-ordering), ... are axioms. ... or if it is aleph-0 x aleph-0 matrix. ...
    (sci.math)
  • Re: A Logical Model for Lists as Relations
    ... To reply to another thread where Bob raised the utility question, ... undoubtful that sequences appear all over the math. ... I have doubts regarding the prevalence of sequences of axioms. ... In the math, sequences and series are very often parameterized so that one can construct statements or descriptions regarding the ith or jth element/term. ...
    (comp.databases.theory)
  • Re: What is a lawlike sequence?
    ... lawlike sequences would not necessarily be a ... or odd if there isn't a set of axioms "defining" ... dealings with Heyting. ... |Intuitionists don't object to the axioms. ...
    (sci.math)