On 9/29/2013 8:06 PM, quasi wrote: > Hetware wrote: >> >> What I am saying is that if I encountered an expression such >> as (t^2-9)/(t-3) in the course of solving a problem in >> applied math, I would not hesitate to treat it as t+3 and not >> haggle over the case where t = 3. > > And you would be wrong unless either > > (1) You know by the context of the application that the value > t = 3 is impossible. > > (2) You know by the context that the underlying function must > be continuous, thus providing justification for canceling the > common factor of t-3, effectively removing the discontinuity. > > I challenged you to find a book -- _any_ book, which agrees > with your naive preconception. > > Math book, applied math book, physics book, chemistry book, > economics book -- whatever. > > If all the books and all the teachers say you're wrong, > don't you think that maybe it's time to admit that you > had a flawed conception about this issue and move on? > > quasi >
I don't answer to the authority of mortals. I answer to the dictates of reason. I say that it is logically consistent to view
(t^2-9)/(t-3) = t+3
as valid when t = 3. If a contradiction can be demonstrated, then the proposition is clearly wrong. Note clearly that I am defining (t-3)/(t-3)=1. I am not appealing to a more fundamental meaning for the algebraic form.