The paper's aim is to reveal the return of the Berkeley paradox of the eighteenth century.
This is a conceptual discussion.
Since, long time ago, the common belief has been that the establishment and development of the theory of limits had provided an explanation for the Berkeley paradox. However, when the authors revisit some of the age‐old problems using the thinking logic of allowing both the concepts of potential and actual infinities, they find surprisingly that the shadow of the Berkeley paradox does not truly disappear in the foundation of mathematical analysis.
Show the incompleteness of the theory of limits, which is not the same as what has been believed in the history of mathematics.
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