Abstract
Continuous functions are defined and their main properties studied. Principal results include the intermediate value theorem and the extreme value theorem. Nuggets include iterations.
A function of a variable quantity is an analytic expression composed in any way whatsoever of the variable quantity and numbers or constant quantities
L. Euler
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Notes
- 1.
It is obvious that such sequences exist if A is an interval, and this is the case in all applications considered in this text. For general sets we must appeal to the so-called axiom of choice of set theory.
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Magnus, R. (2020). Functions and Continuity. In: Fundamental Mathematical Analysis. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-030-46321-2_4
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DOI: https://doi.org/10.1007/978-3-030-46321-2_4
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