《数学分析》章节试读

《数学分析》的笔记-第28页

Mathematical Analysis studies concepts related in some way to real numbers.
Real numbers, one method starts with the positive integers 1,2,3..., as undefined concepts and build them a large system, the positive rational numbers(quotients of positive integers), their negatives and zero. The rational numbers, in turn, are then used to construct the irrational numbers, The rational and irrational numbers together constitute the real-number system.
In most of phases of analysis it is only the properties of real numbers that concern us, rather than the methods used to construct them.
The notation x∈S means that the object x is in the set S, and we write x∉S to indicate that x is not in S.
A set S is said to be a subset of T, and we write S⊆T, if every object in S is in T, we said is nonempty if it contains at least on object.
The set R satisfy the ten axioms fall in a natural way into three groups as the field axioms, order axioms, and the completeness axioms(also called the least-upper-bound axiom or the axiom of continuity).