Descriptive definitions of potential and actual infinities
Wujia Zhu, Yi Lin, Ningsheng Gong, Guoping Du · Kybernetes · 2008
Purpose The paper's purpose is to analyze the concepts of potential and actual infinities. Design/methodology/approach The exploration and research on potential and actual infinities generally touch on many disciplines, such as philosophy, logic, computer science, mathematics, etc. From the angle of a brief history, recall and development, the authors analyze the concepts of potential and actual infinities on one starting point and two locations to cut in. Findings Clarify the difference and connection of these two infinities on the level of mathematics and introduce the symbolized, descriptive definitions for potential and actual infinities. Originality/value It is the first time that the difference between the concepts of potential and actual infinities are clarified, which leads to the discovery of the fourth crisis in the foundations of mathematics.