On Saturday, September 28, 2013 1:15:47 PM UTC-7, Hetware wrote: > > 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.
But you are not setting up an equation in physics. You are attempting to learn calculus.
Professor Thomas has a very good reason for showing you this trivial-seeming example of a function with what is known as a "removable singularity". If you are patient and continue to study his book you will find his reasons. Here's a hint: the function sin(x)/x has the same feature at x = 0.
> > 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 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.
Of course it does not contradict the definition of a single valued function of one variable. It contradicts the definition of one particular function, namely Professor Thomas's F(t). The fact that this all seems totally arbitrary to you is just because you don't know the whole story yet.