I don't think they even use the word approaches after calculus 1. In most analysis you would say it converges to something. For this sequence Lim n-->oo An=A we would say that {An} converges to A. Note that {An} is sequence, and A is the limit of the sequence. Also note that this is not confined to the extended real number system, and clearly your case is. Instead of dragging on with too much rigor I would just like to say that you are not talking about something that always has a graph, you are simply talking about a sequence so you need to stay more general if you are going to talk about the notation.
Cheers, Adam
"Paul Lutus" <nospam@nosite.zzz> wrote in message news://MRiO7.39470$ox2.2829787@bin4.nnrp.aus1.giganews.com... > "Chan-Ho Suh" <csuh@math.ucla.edu> wrote in message > news://3C099B3D.8A447554@math.ucla.edu... > > > > > > Paul Lutus wrote: > > > > > "Chan-Ho Suh" <csuh@math.ucla.edu> wrote in message > > > news://3C082CE3.B54ECB73@math.ucla.edu... > > > > > > > Lutus is incorrect. > > > > > > Post your erroneous argument first. > > > > I have posted no erroneous argument, nor do I intend to ever do so. > > > > > > > > > > > > The equal sign refers to equality of numbers. > > > > [gibberish snipped] > > Gibberish on which every skilled poster agreed. Read the thread. Trolls and > mathematicians differed on the result, and the mathematicians finally and > reluctantly agreed with my interpretation. > > > > The example under discussion -- > > > > > > lim x -> 0, 1/x = infinity > > > > > > > Oh, you're doing the "I'm wrong but don't want to admit it so I'll change > the > > discussion topic" approach. Note that 0 and infinity were switched in the > > original post I responded to. > > Read the thread. Don't repeat arguments that have been resolved. The > analysis applies to both. Do you really think these two examples: > > lim x->0, 1/x = infinity > > and > > lim x->infinity, 1/x = 0 > > can meaningfully assert a different meaning for "="? In the above limit, "=" > actually means "approaches." In the lower limit, the same. Otherwise each > statement of a limit applies different symbolic definitions ad hoc. > > To the question "what does 'equals' mean in the above expressions?", will > you now argue that the answer is, "that depends on the specific values that > are present"? > > Think before replying. > > -- > Paul Lutus > www.arachnoid.com > > > >
