Limits and Continuity

George McCarty
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George McCarty: University of California

Chapter 3 in Calculator Calculus, 1982, pp 27-36 from Springer

Abstract: Abstract 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, x2→y, we have ƒ(x2)→ƒ(y). We may also express this by writing $$\mathop {\lim }\limits_{x \to y} f(x)\; = \;f(y)$$

Date: 1982
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DOI: 10.1007/978-1-4684-6484-9_3

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