In article <9u8llf$a2e$1@flotsam.uits.indiana.edu>, glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) writes: >In article <9u8c70$ked$1@wisteria.csv.warwick.ac.uk>, > <mareg@primrose.csv.warwick.ac.uk> wrote: >>In article <20011130094007.686$Ng@newsreader.com>, >> David W. Cantrell <DWCantrell@sigmaxi.org> writes: >>> >>>I think it quite regrettable that the correct intuition of children is >>>often quashed by some teachers (well meaning, but ignorant) who insist >>>that statements such as 1/infinity = 0 are nonsense. >> >>I don't - I find it admirable! I think sloppy imprecise thinking should >>be discouraged at as early an age as possible. > >Must we really insist that the children say limit(x->oo) 1/x = 0?
Well if that is what they really mean when they say 1/oo = 0, then yes, certainly. I think they should be encouraged to say what they mean. On the other hand, if they are envisaging an extended real number line with an actual object named infinity in it, then they should be warned that they need to proceed with care, and asked what they think 0 times oo is equal to.
In any case, they should be asked to explain exactly what they mean by 1/oo = 0.
