[미적분] 칼큘러스(미적분학) 정의들(Definition)

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미적분학의 정의들을 정리하논 영문자료입니다.

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본문내용

Definition of an inductive set. : A set of real numbers is called an inductive set if it has the following two properties.
(a) The number 1 is in the set.
(b) For every x in the set, the number x + 1 is also in the set.
∴ Definition of Positive Integers. : A real number is called a positive integer if it belongs to every inductive set.
∴ Definition of Least Upper Bound. : A number B is called a least upper bound of a non-empty set S if B has the following two properties.
(a) B is an upper bound for S
(b) No number less than B is an upper bound for S.
∴ Axiomatic definition of area. We assume there exists a class of measurable sets in the plane and a set function a, whose domain is , with the following properties:
1. Nonnegative property. For each set S in , we have a(S) ≥ 0.
2. Additive property. If S and T are in , then S∪T and S∩T are in , and we have a(S∪T) = a(S) + a(T) - a(S∩T)
3. Difference property. If S and T are in with S⊆T, then T-S is in , and we have a(T-S) = a(T) - a(S).

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