On Sunday, September 29, 2013 5:30:49 PM UTC-7, Hetware wrote: > 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. > > > > I can't show you a book that explicitly tells me I can do this, but I > > can cite one that tells me that I can get away with it, until you prove > > a contradiction: > > http://books.google.com/books/about/Grundz%C3%BCge_Der_Mathematik_Fundamentals_o.html?id=1N0lMwEACAAJ
So, logically, you know what is the value of f = 0/0? According to the definition of division ('/'), f is that number which, when multiplied by the denominator (0 in this case) gives the numerator (also 0 in this case). So, you want an f that gives you 0*f = 0. That is the DEFINITION of division! (If you insist on being logical, you should insist on starting with the definition.) So, tell me: what is the value of f, and why do you claim that value?