Re: infinity

In article <MPG.1d8a1fc94761f8f698a230@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> Virgil said:
> > In article <MPG.1d88e60baef09fd398a207@xxxxxxxxxxxxxxxxxxxxxxxxx>,
> > Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:
> >
>
> > > I suppose I can live with an image with no leaf nodes, but that
> > > doesn't affect the relationship between branches and paths, does
> > > it?
> >
> > Yes it does! In trees in which every path has a leaf node, there is
> > an obvious bijection between paths and leaf nodes, but in a maximal
> > binary tree there are infinitely many paths and zero leaf nodes. If
> > that correspondence fails so dramatically in the "lomiting" case,
> > what is TO's evidence that any others still hold?
> >
>
> I don't think that the leaf nodes automatically disappear when the
> tree is infinite.

Then where are they? A path with no last node cannot have a last node,
and that is what a leaf node has to be. If it is not the last nnode of
some finite path, then it is not anywhere.

When one extends a path through a leaf node to another node, the leaf
node ceases to be a leaf node. When a path is extended unendingly, there
is no end. That is what unending means.
.

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