Limit problem, theory very basic question

[flyingpig]

Homework Statement

I remember I got it wrong way back in calculus I over this concept.

If I have

lim f(x) = ∞
x→∞

Would it be right to say the limit does not exist? I remember my professor said it was wrong because it does exist and it is infinity.

 

[Harrisonized]

It doesn't exist on ℝ. However, it does exist on ℝ∪{−∞, +∞}. The latter is usually written as ℝ with a bar over it, but I don't know how to type that.

 

[HallsofIvy]

Harrisonized is talking about the "extended real number system". But, in Calculus, you seldom mention that. Typically, in calculus, it is best to think of "$lim f(x)= \infty$ as just meaning "f(x) does not have a limit (for a particular reason)".