Re: An infinite debate


"Tony Orlow" <tony@xxxxxxxxxxxxx> wrote in message
news:455388d9@xxxxxxxxxxxxxxxxxxxxxx
David Marcus wrote:

Um, what if you start with 0, increment it at 1 minute before noon, then
again at a half minute before noon, then again at a third of a minute
before noon, etc, so that at time noon-1/n the number achieves a value of
n, for n in N? That way we have counted through all of the natural numbers
by noon, correct? What is the value of n at noon?

This is a great question and I think the answer to it depends on what is
meant by `increment' and what is meant by the value of `n' at noon. If by
`n' we mean a variable name for a number stored in the registry of some kind
of ideal computer then I don't think the value of `n' at noon is defined.
But what if by `n' we mean the number of hash marks that could be made in a
unit interval by noon? That is at 1 minute before noon a hash mark is made
at the location -1 on the real line, at 1/2 minute before noon another hash
mark is made at -1/2 on the real line, at 1/3 of a minute before noon yet
another hash mark is made at -1/3 on the real line, and so on. At noon the
total number of hash marks in the interval [-1,0] should be ALEPH_0.

All the best,
R






.

Loading