Re: the binary tree
- From: calvin <crice5@xxxxxxxxxxxxxx>
- Date: Fri, 17 Apr 2009 08:41:58 -0700 (PDT)
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.
.
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