Ben Bacarisse
4/29/2011 3:51:00 PM
James Kuyper <jameskuyper@verizon.net> writes:
<snip>
> I also think that it might be better to replace "contiguous" with
> "consecutive". "contiguous" seems, to me, to have primarily spatial
> connotations, while "consecutive" is a temporal relationship.
I don't get such a strong indication of temporal vs. spacial here. The
OED backs up this intuition in that there is a second definition for
"contiguous":
2. Next in time or order, immediately successive.
However, consecutive can carry a more abstract meaning that matches
what seems to be required here:
2. Consisting of elements following in order; characterized by
consecution or logical sequence.
So I agree but for slightly different reasons.
The strongest distinction I get (again just an intuition) is this: the
positive integer subset of the reals are consecutive but not contiguous.
The intervals [n, n+1) with n a positive integer are contiguous and
consecutive, whilst a set of regions that tile the plane are contiguous
with necessarily being consecutive. In other words, one is is to do
with covering without gaps, and the other implies a logical or natural
sequence. These meanings are certainly there in the dictionary, but
there are enough other meanings that this is not the only way to read
the words.
<snip>
--
Ben.