Re: infinity

k wallace wrote:
> if the following is utter bunk, please explain.
> If you are saying there's an infinite string, you must have a way to
> define it. As far as I know, have read, etc., the only way to think
> about infinity is "there's always a number one greater", which is not a
> hard statement to say mathematically- say, if x is a number y digits
> long, then x + 1 is a number y + 1 digits long, and x and y are known, 1
> is known, so how can numbers be infinite in string length?

Exactly right. They can't, at least not anything that qualifies as a
single "number" or "numeric value".


> Did I miss something? It (the above) sounds logical, but it is also not
> impossible to imagine that 'infinite' length could be possible. It's
> certainly not like we can find, or define, an infinite- or even largest-
> number (real, natural, whole, or any other kind).

*If* there were a natural (counting) number of infinite length (i.e.,
of infinite value), there could be only one such number, for the simple
reason that, it being the largest number, there could be no larger
number than it. If W exists, and there is no Y > W, then there must
be only one W.

But supposing that such a critter exists leads to contradictions
and violations of the definition of "number".


On a related note, it may sound counterintuitive to say that N,
the set of natural counting numbers, is an infinite set containing
only finite numbers. It might seem that in order for N to be of
infinite size, it must contain at least one infinite number.
But this is not the case; N is simply an unending set of finite
numbers, there being no largest or last number in the set. For
whatever number x you choose as a member of N, there is always a
larger member x+1. N is infinite because it has no last member.

-drt

.

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