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On Thu, 17 Jan 2013 19:50:37 -0800, Gary Shannon <[log in to unmask]> wrote:

>On Thu, Jan 17, 2013 at 7:19 PM, Roger Mills <[log in to unmask]> wrote:
>> At risk of repeating what others may have said, it isn't that English
>> sentences can be "infinite" in length; it is that there is an _infinite
>> number_ of possible English sentences (or any other natlang).
>
>Without either an infinite lexicon, or the possibility of an
>infinitely long sentence, there cannot be an infinite number of
>possible sentences.

Without either an infinite number of digits, or the possibility of an infinitely long integer, there cannot be an infinite number of possible integers.  After all, assume a set of ten digits, like we use day-to-day.  Allowing integers of N digits, there are only 10^N possible integers: large, but not infinite.   :-p

Alex