Basing on the model-theoretic properties of having algebraically prime models and being simply closed for first-order theories,we present new proofs for quantifier elimination of theories of complete forked trees,including theory of complete k(k<ω)-ary trees and of complete infinite-ary trees, which simplify original proofs extremely.

Does the Largest Natural Number Exist?——A new method in infinity theory to eliminate the paradox of transfinite numbers(2)

Second all the problems and paradoxes related to infinitesimal,infinitely great and infinity concepts in the classical infinite theory are.

The Puzzling of Infinitude and Precise Definition of Limit;

The perfectibility of the definition about the infinitude in mathematics was analyzed firstly in this paper.

Eastern and western series in Qingtimes is comparatively studied and the opinions are that the eastern traditional mathematics,different from westerns,are lack of the characteristic that distinguish from science,so the eastern and the western conception of infinite made different progress.

Ancient Chinese mathematicians had tried to extend them as for as infinite arithmetic,but the result turned out to be a set of formal operations corresponding to polynomial theory.

This paper,we generalize definition of recurring constant,and discuss the line integrals of a function on non-simply connected region with infinite number of holes.