Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

No limit

  1. Oct 2, 2007 #1
    f(x)=1,xeQ
    f(x)=0,x in not eQ

    It's easy to understand that this function has no limit as x tends to 0,but how we can prove it with mathematical formulas.

    And what's the lim[e^n-(1+1/n)^n^2]
     
    Last edited: Oct 2, 2007
  2. jcsd
  3. Oct 2, 2007 #2

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Prove it with the definition of limit.

    Can you find an epsilon such that no delta-nbhd of 0 is mapped entirely in an epsilon-nbhd of f(0)=1?

    Or use the characterisation in terms of sequences. The limit is f(0) iff for every sequence converginf to 0, the image sequence converges to f(0). Can you find a sequence such that the image sequence does not converge to f(0)?
     
    Last edited: Oct 2, 2007
  4. Oct 3, 2007 #3
    quasar987,
    I could not solve with sequences.Can u plz post the solution.
     
  5. Oct 3, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    So far you haven't shown that you have tried anything at all! What have you tried?

    Have you thought about what f(x) is if x is close to 0 and rational?
    What f(x) is if x is close to 0 and irrational?
    COULD f(x) be "close" to some limit if x is any number close to 0?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: No limit
  1. Limit of (Replies: 13)

  2. Limit of this (Replies: 21)

  3. Limit ? (Replies: 2)

  4. Limit of a limit? (Replies: 24)

Loading...