"Dirk Van de moortel" <email@example.com> wrote... > John Gabriel <firstname.lastname@example.org> wrote:
> Take the function f(x) = 1/x.
Dirk, as you know you are spoiled for choice here. The clunkhead might think - who knows - you've found the only function showing up his system for what it is.
> See if you can prove continuity at x=1 with *your* equivalence: > For all epsilon > 0, Exist delta > 0, such that for all x: > |x-1| < delta <==> |1/x-1| < epsilon > > Take epsilon = 2. > Give me that delta,and I'll give you an x that does > NOT satisfy the equivalence.
When there are this many holes, there is no point trying to thread together what material there is that is cogent.
It's a bit like trying to cover a plane with rationals. (-: