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

Continuity definition

  1. Feb 16, 2010 #1
    I'm just wondering why in the definition of continuity, limit of function, or even just limit of a sequence, the inequality signs are strict? What would happen if you only required that
    [tex] | f(x) - L |\leq \epsilon[/tex]. Or that [tex]|x-a|\leq \delta [/tex].
     
    Last edited: Feb 16, 2010
  2. jcsd
  3. Feb 16, 2010 #2

    mathman

    User Avatar
    Science Advisor

    Without giving it much thought, I suspect it doesn't matter whether the inequalities are strict or not.
     
  4. Feb 16, 2010 #3
    So it was simply decided that the definition had this: it's just convention then? There is no special case that required them to be this way?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook