"Hetware" <firstname.lastname@example.org> wrote in message news:lNGdnf7IAoJV1s7PnZ2dnUVZ_gmdnZ2d@megapath.net... > On 10/7/2013 4:56 AM, David Bernier wrote: >> On 10/07/2013 03:21 AM, Robin Chapman wrote: >>> On 07/10/2013 04:34, Hetware wrote: >>>> On 9/30/2013 4:03 AM, Robin Chapman wrote: >>> >>>>> Hetware: 0/0 = 3 >>>>> >>>>> Ciekaw: 0/0 = 1 >>>>> >>>>> Any more entrants? >>>> >>>> To be correct; Hetware: 0/0 = 1 (under certain circumstances). >>> >>> Not according to your original posting in this thread :-( >> >> Heware, if 0/0 = 1, then 0/0 = (100*0)/0 = 100*(0/0) = 100*1 = 100. >> >> So, assuming 0/0 = 1, we find that 1 = 100 :( > > That statement came with a qualification. That is, given a function > defined by f(t) = (t^2-9)/(t-3), I could assume (t-3)/(t-3) = 1, even > where t=3. I've already shown that a modified version of that proposition > does make sense.
Be reassured, it doesn't.
> Given a function f(t) continuous for all real numbers t and defined by > (t^2-9)/(t-3) everywhere the expression is meaningful
I.e. for t!=3, so f isn't actually defined for all t, and even less it is continuous for all t.
> , that function is identical to g(t) = (t+3).
So, it isn't: g *is* defined and continuous for all t in R.
You keep thinking that f and g must be equivalent functions, but they aren't.
> My original mistake was to assume continuity after using (t^2-9)/(t-3) to > define the entire function.