# Thread: Theoretical question on infinity and limit

1. ## Theoretical question on infinity and limit

Is it correct to say that when the degree of the numerator is greater than the degree of the denominator with x approaching infinity, that limit is infinity or limit does not exist
My question is: when limit is infinity, does it mean that limit does not exist?

Thank you very much

2. The thing is: existence of a limit will depend of one sided limits.

If the limit is $\infty,$ this does not say the limit does not exist.

A simple example: consider $\underset{x\to 0}{\mathop{\lim }}\,\frac{1}{x}.$ Since $\underset{x\to 0^{-}}{\mathop{\lim }}\,\frac{1}{x}=-\infty$ and $\underset{x\to 0^{+}}{\mathop{\lim }}\,\frac{1}{x}=\infty$ then the limit does not exist 'cause both one sided limits are different.

3. Originally Posted by oceanmd
Is it correct to say that when the degree of the numerator is greater than the degree of the denominator with x approaching infinity, that limit is infinity or limit does not exist
My question is: when limit is infinity, does it mean that limit does not exist?

Thank you very much
Yes. Since "infinity" is not a real or complex number, saying that the "limit is infinity" is just a way of saying the limit does not exist in a particular way.