Limits and Continuity

  • George McCarty


We have been assuming up to now that the functions we were working with were “continuous.” That is, we have assumed that if ƒ(r)=0 and x0, x1, x2, … were numbers that got closer and closer to r, then the numbers ƒ(x0), ƒ(x1), ƒ(x2), … would get closer and closer to ƒ(r) = 0. More generally, a function ƒ is continuous if for each point y and each sequence x0, x1, x2 … = x2 that has y as limit, x2y, we have ƒ(x2)→ƒ(y). We may also express this by writing
$$\mathop {\lim }\limits_{x \to y} f(x)\; = \;f(y)$$


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Copyright information

© EduCALC Publications 1982

Authors and Affiliations

  • George McCarty
    • 1
  1. 1.University of CaliforniaIrvineUSA

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