On 9/29/2013 3:16 AM, quasi wrote: > Hetware wrote: >> >> So the answer is consensus among mathematicians holds that >> F(t) = (t^2 - 9)/(t - 3) is undefined at t = 3? > > Yes. > >> 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. > > Then _define_ it as F(t) = t + 3. > > If simplifying (t^2 - 9)/(t - 3) to t + 3 is correct in the > context of your application, then simplify it in advance before > defining the function. > >> and do not expect any adverse consequence from doing so. > > If the physical context makes removable discontinuities > impossible, then _remove_ them. Don't leave them there in > the definition of the function. > > quasi >
I am not familiar with a definition of /function/ which tells me the order in which sub-expressions should be evaluated. A function is a mapping. My interpretation works as a mapping of -oo < t < oo.
I agree that 0/0 is meaningless out of context. But (t-3)/(t-3) provides a context. Now, I might be putting the cart before the horse by considering the context because that is implicitly using the concept of a limit.
I would need a lot more in the way of formal development than a typical calculus book provides in order for me to be convinced of the error of first evaluating (t-x)/(t-x) symbolically and then evaluating it for an actual argument.
If I were to write a computer program for processing functions defined in terms of algebraic expressions, I could write it so that it simplifies then evaluates, or I could write it so that it evaluates "as is".