数学哲学——现有极限论的三大缺陷

onnecting with the long existing problems in infinite theory and limit theory exposed by suspending Zeno’s Paradox, Berkeley’s Paradox and Russell’s Paradox as well as Cantor’s two logical mistakes in set theory, the close relationship between the defects in present infinite theory, number system and the defects in present limit theory are studied. The long neglected defects in the foundation of present classical limit theory of its theoretical system, qualitative operation and quantitative operation are analyzed． Three fatal defects in the present classical limit theory are disclosed: present classical limit theory is unsystematically in both theory and operation; it is unable to carry out its qualitative operation; it is unable to carry out its quantitative operation.