In article <firstname.lastname@example.org>, quasi <email@example.com> 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
Note that the standard rules of evaluating algebraic expressions require that all operations enclosed within any set of parentheses be performed BEFORE any operation combining that result with any other result.
Thus '(x^2-9)/(x-3)' requires that both '(x^2-9)' and '(x-3)' be evaluated before the division can be performed.
Thus if F(x) = (x^2-9)/(x-3), then F(0) MUST be first reduced to 0/0, at least according to the rules of algebra, before that division can properly be addressed. --