Re: Cantor and the binary tree

In article <MPG.1cff9fda6b659940989d2e@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow (aeo6) <aeo6@xxxxxxxxxxx> wrote:

> If someone wants to tell me that one can't insert a node in the tree, I
> suggest
> they ask their programmer friends, before wasting my time.

Inserting nodes in trees is quite possible in general, but when doing it
in binary trees, one may make them into non-binary trees, and in a
binary tree in which no path has a leaf node, it will necessarily make
it into a non-binary tree.

So that inserting nodes into such maximized binary trees is irrelevant
to the number of nodes or the number of unleafed paths in such a tree.

In a maximal binary tree, the set of nodes easily bijects to N and the
number of unleafed paths easily bijects to P(N), and Card(N) < Card(P(N))
.

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