Re: the binary tree

On Apr 17, 10:41 am, calvin <cri...@xxxxxxxxxxxxxx> wrote:
On Apr 17, 11:29 am, Dave <dave_and_da...@xxxxxxxx> wrote:

On Apr 17, 8:23 am, calvin <cri...@xxxxxxxxxxxxxx> wrote:

Yes, but so what?  The binary tree yields the uncountable
number of reals between zero and one in a countable
number of construction steps.

Please demonstrate the first several layers of this binary tree.

It's just the standard binary tree:

Under each node, consider the left branch to be a zero
and the right branch to be a one.  At the end of each
branch is a node, from which drop two more branches,
another zero and one.  Under the topmost node, where
I place the binary point, is the first row, consisting
of two branches ending in two nodes.  Under that is the
second row, consisting of four branches and four nodes;
under that is the third row, consisting of eight branches
and eight nodes.  And so on.

Are there values in the nodes? If so, what are they? If not, where do
all the real numbers lie?

Dave
.

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