On Tue, Sep 4, 2012 at 1:10 PM, William R. Buckley

While at any moment the tape may be finite, that it can at need grow is the
> fundamental notion of infinite.

No, the fundamental notion of the infinite is that you can make a one to
one correspondence with a proper subset of itself.

> The net result of Turing’s specification is that the tape is  infinite

If the machine comes to a halt then a finite amount of tape is sufficient
to get its work done, if it does not halt then even a infinite amount of
tape would not be sufficient. Turing proved that there is no general way to
tell in advance one case from the other.

  John K Clark

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