> > So the answer is consensus among mathematicians holds that F(t) = (t^2 - > 9)/(t - 3) is undefined at t=3? Perhaps what I should have said at the > outset is something along the lines of: on any given day, if I'm setting > up an equation in physics, and produce an expression such as F(t) = (t^2 > - 9)/(t - 3), I treat it as t+3, and do not expect any adverse > consequence from doing so. > > If I conceive of mathematics as an exercise in defining and manipulating > symbols, it seems that declaring constructs such as F(t) = (t^2 - 9)/(t > - 3) to be undefined at t=3 is arbitrary. The fact that there is an > obvious candidate for a value of F(t) at t=3
Since 3 isn't in the domain of F there is no candidate obvious or otherwise.
> tells me that accepting > that candidate as the value at t=3 does not contradict the definition of > a single valued function of one variable. > >
-- The world will little note, nor long remember what we say here Lincoln at Gettysburg