Yes dividing by 0 is all you need to do to make a function undefined at a point. Removeable singularities are good examples because they illustrate the point without being overly pathological.
Your "obvious" reasoning is wrong, [tex]f(x) \neq x + 1[/tex] in order to make your simplification you implicitly assumed that [tex]x\neq 1[/tex], and that's the entire point isn't it! Of course you lose the subtlety if you do bad math! lol
If I'm understanding this defintion right, it implies continuity (or defines it...) I'mprobably overthinking it if I'm making conclusions like that. I'll set it asides and try to figure it out another time.
Anyway, many thanks for the attempts at explaining.
I can't get my head around the epsilon-delta definition of a limit. Unfortunately I don't have a teacher to ask (I'm teaching this to myself as a self interest) so this forum is my last resort -- google hasn't been kind to me.
From what I've seen, I don't really understand how the definition means much of anything (visual examples included.) All it seems to say is "there is an unspecified value which is greater than the difference between a function and a given value L, where that difference is greater than zero" The problem is, I don't see any need for L or f(x) to be anywhere near one another.
Deacon John, can you tell me please using your definition of limit what IS the following limit.
1) lim 2x+1 as x-------> 2 where f:N------>R where N is the natural Nos and f(x)=2x+1
Does the following function has any limits within its domain and if yes how many???