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1.近年来,数学中的构造方向获得了重大的进展,它的实貭是局限于不引起实无穷性抽象的潛在能行性的抽象的范围內,而仅仅限于研究构造性对象。同时,由于对具有給定性貭的对象的存在,只是在指出了构造这种对象的潛在能行性的方法之后才被认可,因此,否弃了所謂純粹存在性的定理。我們不去給构造性对象的概念下定义,而只給予解释,构造性对象是指某些图形,它是由另一些基本的图形——基本的构造性对象——按一定方式来組成的。用儿童积木“建筑师”构筑起来的建筑物,以及由继电器所組成的继电器接触线路,就是这种例子。在构造性数学理論中,为了避免作出构造性对象的一般定义,我們局限于研究某些标准型式的构造性对象,无論是构成我們結构的零件——基本的构造性对象,还是基本的构造性对象的結合方法,都应当标准化。最簡单的一种构造性对象,就是在一个确定的字母表中,由它的字母所构成的字。在給定字母表中的字,就是其中字母的一个序列。例如,
1. In recent years, the structural direction in mathematics has made significant progress. Its practicality is confined to the range of abstractions that do not lead to real abstractions of potentiality, but only to the study of constructive objects. At the same time, since the existence of an object with a given ambiguity is recognized only after pointing out the method of constructing the potential of such an object, the so-called pure existence theorem is abandoned. We do not define the concept of constructive objects, but only give explanations. Constructive objects refer to certain figures. They are composed of other basic figures—basic constructive objects—in a certain way. Buildings constructed with children’s building blocks “architects” and relay contact lines made up of relays are examples. In the theory of constructive mathematics, in order to avoid making the general definition of constructive objects, we are confined to the study of certain standard forms of constructive objects, whether they are parts of our structure - basic constructive objects or basic constructs. The method of combining sex objects should be standardized. The simplest kind of constructive object is the word formed by its alphabet in a certain alphabet. The word in a given alphabet is a sequence of letters. E.g,