Let’s see following three incoherent situations:

(a) During the quantitative cognizing calculation process in dealing with "infinitesimal variables or monads”, all of a sudden someone cries out “let them be zero or get the limit or get the standard number” to those “busy acting” variables or monads. So, the very variables or monads suddenly lost completely "Archimedean Property", and no further participations are allowed in the very calculation process and, being derived away suddenly from the formula is to be the only result. This situation has been existed since ancient times in mathematics, it is Berkeley who made up Berkeley’s Paradox (discover all the suspended members of the Berkeley’s Paradox Family), sharply and bravely pointed out the fundamental defects disclosed by such paradoxical operation!

(b): during the quantitative cognizing calculation process in dealing with "infinitesimal variables or monads”, no one dare to cry out “let them be zero or get the limit or get the standard number”. So, "infinitesimals or monads" will never lost "Archimedes", they will stay in the very calculation process forever and join all the calculating operations with the property of "Archimedean Property". This situation has been existed since ancient times in mathematics, it is Zeno 2500 years ago who made up huge suspended Zeno’s Paradox Family (such as the newly discovered Paradox of Harmonic Series, the Gabriel Axis Paradox of paint with infinite area in a finite volume,...), sharply and bravely pointed out the fundamental defects disclosed by such paradoxical operation!

(c): during the quantitative cognizing calculation process in dealing with "infinitesimal variables or monads”, whenever infinite variables or monads appear someone cry out “let them be zero or get the limit or get the standard number”. So, no calculations are needed and there would be no mathematical analysis at all. Of course, the success of applied mathematics dictates that this is never being allowed.

So, in present classical mathematics analysis, many quantitative cognizing calculation processes and their results in dealing with "infinitesimal variables or monads” are certainly to become paradoxes -------either members of the Zeno’s Paradox Family or members of Berkeley’s Paradox Family.

This is why we are so sure to say that the Second Mathematical Crisis in present scientific theory system is unsolvable!

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