Re: Turing completeness of the functional paradigm?

Mr Elliot wrote:
> > > Peano's axioms allows a well ordering, indeed a sequential ordering, of
> > > the integers. So in this sense, Peano's axioms do impart a spacial
> > > orientation, that the integers can be strung along a line like
> > > cloth pins on a cloth line.
> >
> > I see. Still, it seems that they impart nothing else.
> >
> It's a natural order. Other orders my be imparted to the integers,
> however they will not be as simple to describe within Peano's axioms.
>
> They could be reversed in order, they could be made into two parallel
> lines, one of even numbers, the other of odd numbers. They could
> be put all odd numbers first with the even numbers coming after all
> the odd numbers.
>
> ,... 4, 3, 2, 1
>
> 1, 3, 5,...
> 2, 4, 6,...
>
> 1, 3, 5,... 2, 4, 6,...
>
> Cantor arranged them to spread over the plane like this
>
> 1 3 6 10 15 ...
> 2 5 9 14 ...
> 4 8 13 ...
> 7 12 ...
> 11 ...
> ...

Yes, right.

> > They all seem to be merely Peano sequences.
> >
> The Peano isn't the only instruement mathematicians play.

Of course. There may be multiple names of the same rose. :-)

> > "The main problem of mathematics is the notion of truth." -- H.C.,
> > Outlines...
> >
> The main problem of philosophy is truth.
> This is an attribute shared by the White-Lie House.
>
> The main problem of art is art critics.
>
> The main problem of eternity is it takes too long.
> The main problem with infinity is finding room for it.
>
> The main problem of nothing is there's nothing to it.

Right.

> Riddle of the Day: Where is everywhere?
> Is it here? Is it there? Is it anywhere?

Mr Elliot, I agree. Now, please, would you be kind enough as to care to
give me an example of a relation which is not spatial. IOW, are all
relations spatial? I think so. But I will not assume that on my own. It
is far far too serious.

Thank you.
Tom

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