On Saturday, September 28, 2013 12:30:42 PM UTC-4, Hetware wrote: > I'm reading a 1953 edition of Thomas's Calculus and Analytic Geometry. > > In it he states that given: > > F(t) = (t^2-9)/(t-3) > > > > F(t) = (t-3)(t+3)/(t-3) = t+3 when t!=3. > > > > But F(t) is not defined at t=3 because it evaluates to 0/0. > > > > If someone were to ask me if (t^2-9)/(t-3) is defined when t=3, I would > > say it is because it can be simplified to t+3. Am I (and/or Thomas) > > engaging in meaningless hair-splitting regarding the question of F(3) > > being defined?
I like to think of the original F as having a bug. For example, if in Python I try to implement the formula as given I get:
|>>> def f(t): (t**2 - 9)/(t-3)
|>>> f(3) Traceback (most recent call last): File "<pyshell#2>", line 1, in <module> f(3) File "<pyshell#1>", line 1, in f def f(t): (t**2 - 9)/(t-3) ZeroDivisionError: division by zero |>>>
Simplification is analogous to debugging (the simplification here can be described as removing a removable discontinuity, which sounds sufficiently close to debugging that I don't think that the analogy is too much of a stretch). A debugged program is manifestly not equivalent to the buggy version. Why should you regard a debugged formula as equivalent to the buggy one?