关键词: calculus, limit theory, potential infinity, actual infinity

Abstract: Refs 1 and 2 provide the definition of the concepts of ‘potential infinity’(poi) and actual infinity(aci); Ref 3 discusses and verifies that poi and aci are a pair of contradictory opposites without intermediate (p,-p).The second part of this paper, i.e., §2, further discusses the manners in which a variable x approaches infinitely to its limit x0 using the poi and aci methods and concludes that, in any system compatible with both poi and aci, the two approaching manners are also a pair of contradictory opposites without intermediate (A,-A). Finally, on the basis of this conclusion, we reexamine the fundamental question of Leibniz’s Secant and Tangent Lines in calculus and the limit theory and offer our analysis and raise new questions. 

Key words: calculus, limit theory, potential infinity, actual infinity