2009•Ziran bianzhengfa tongxunRequires access
Analysis of the Potential Infinity and Actual Infinity
Guoping Du
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Abstract
What is the potential infinity,what is the actual infinity,and what is the relation between them? There has been a long history of the contest between the potential infinity and actual infinity from the the birth of infinite concept.Although different philosophers,logicians and mathematician have different viewpoints of infinity,but they gave only the intuitional description and they didn't give the strict mathematic definition for the potential infinity and the actual infinity in history.We are unable to decide which is right for the relation between the potential infinity and the actual infinity.By analysis the character of the potential infinity and the actual infinity,we attempted to give a strict definition of the potential infinity and the actual infinity,we can use this definition to re-explain the paradox and provide a new angle of view for studying the set theory.