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Math Help - Theoretical question on infinity and limit

  1. #1
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    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
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by oceanmd View Post
    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.
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