Re: Fast creation of a set (was: Strange machine-level exception)
Juergen Luethje wrote:
>
<snipped/>
>
> Mathematically speaking, a set is a "collection of objects in which
> order has no significance". <<a
> href="http://mathworld.wolfram.com/Set.html">http://mathworld.wolfram.com/Set.html</a>>
> So no application should rely on the assumtion that the elements in
> a set are in a particular order, shold it?
>
This is true. However, any bijection between a set and an ordered set gives the
source set an ordering.
Hence, an application may define any sort of order on a set if it is convenient
in any way. After all, there is an order relation on all Euphoria objects,
defined by:
x < y <===> compare(x,y)=-1
And since all sets we deal with in computer world are finite, hence mappable to
some starting section of |N, there is always a natural way to order any set we
encounter.
It is easy to see that any set of objects can be considered part of a set of
cardinality aleph_n, with {\it n} the maximum sequence nesting level in said
collection of objects. And there is a natural order relation over such a set,
built recursively starting from the natural ordering of integers. (Over |R (n=1),
this is the ordering of reals by their continued fraction).
CChris
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