email@example.com (Herman Rubin) wrote in <a href="news://firstname.lastname@example.org:">news://email@example.com:</a>
>>Should we now argue that there should be only one definition for each >>term? I mean, why define continuity using epsilon-delta? > > We definitely should not; even for one variable, intervals > are easier. > > Wouldn't it be nicer if >>we just defined it using preimages of open sets? > > One could, but this would be more difficult than the > existence of a neighborhood mapping into a neighborhood. > This is the one which carries over to uniform spaces, > for example. >
You did catch the part where I said I was using sarcasm to make a point? I was trying to show that often times, having multiple ways to express something, or multiple definitions actually make things easier.
-- Timothy M. Brauch NSF Fellow Department of Mathematics University of Louisville