Results 1 to 3 of 3

Math Help - Infinity and the Real Number Line

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    158

    Infinity and the Real Number Line

    Is infinity an element of the real numbers?

    I know that infinity is a concept that denotes larger and larger numbers on the real line, but I was given a definition of a limit as being a finite element of the real numbers but now I have seen examples where the limit of a function has turned out to be infinity. So does this mean that infinity is an element of the reals or is the definition that I was given completely wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Noxide View Post
    Is infinity an element of the real numbers?

    I know that infinity is a concept that denotes larger and larger numbers on the real line, but I was given a definition of a limit as being a finite element of the real numbers but now I have seen examples where the limit of a function has turned out to be infinity. So does this mean that infinity is an element of the reals or is the definition that I was given completely wrong?
    What you were given is completely wrong. The concept that \lim_{x\to c}f(x)=\infty is shorthand notation that can wreak havoc on the untrained mind. Saying that \lim_{x\to c}f(x)=\infty does not mean that the limit "equals" some number " \infty". What it does mean is that given any M\in\mathbb{R} one can find a \delta>0 such that |x-c|<\delta\implies |f(x)|>M. In other words, to say that a limit is infinite means you can make f(x) arbitrarily large by making x sufficiently close to c.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,646
    Thanks
    1596
    Awards
    1
    There is an excellent discussion of this confusing topic in Ken Rossís Elementary Analysis textbook.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. real analysis proof of divergence to -infinity
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: June 22nd 2011, 01:57 PM
  2. Replies: 11
    Last Post: November 14th 2010, 07:33 PM
  3. interval on real number line
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 28th 2010, 05:26 PM
  4. any number can divides infinity???
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: August 19th 2009, 11:58 PM
  5. Proof. Real number line.
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 13th 2008, 11:53 AM

Search Tags


/mathhelpforum @mathhelpforum