From LOJBAN%CUVMB.BITNET@UBVM.CC.BUFFALO.EDU Tue Dec 5 19:37:44 1995 Reply-To: Dylan Thurston Date: Tue Dec 5 19:37:44 1995 Sender: Lojban list From: Dylan Thurston Subject: logarithms X-To: "Steven M. Belknap" X-cc: LOJBAN%CUVMB.BITNET@cmsa.berkeley.edu To: John Cowan In-Reply-To: Status: OR Message-ID: On Tue, 5 Dec 1995, Steven M. Belknap wrote: > >la stivn cusku di'e > > > >> A challenge to all: produce a gismu which can not be considered to be fuzzy . > > > la xorxes cusku di'e > >There are some (e.g. dugri, tenfa, sinso, tanjo) for which it wouldn't be > >very easy to consider them fuzzy. > > > No dice. Fuzzy numbers and fuzzy arithmetic can be easily extended to > logarithms, exponentials, and trigonometric functions by expressing the > Reimann remainder term at the end of the Taylor Series expansion as a fuzzy > interval. ... Certainly operations on fuzzy numbers are well-defined (and quite useful for, e.g., doing mathematical proofs by computer and keeping track of the possible error). But I don't see the relevance. When I say '2 is the log base 2 of 4', I'm making an exact statement. There's no fuzziness whatsoever about it. It would be absolutely false to say '2.00000000001 is the log base 2 of 4.' So the fuzziness you refer to is not due to the predicate 'dugri', but to the fuzziness of its arguments in some specific application. co'o mi'e dilyn.