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