Analysis of Switching Resistive Circuits

To date, it is well known that it is impossible or at least meaningless to divide a number by zero. In the same respect,
we are allowed to multiply by zero, to add zero, and to subtract zero. In other words, some operations with zero are allowed. Where does such a contradiction originates from, what is zero? Are the properties of zero responsible for such a no-go or today's valid mathematical rules, we have to take into account while operating with zero, or both or none?
Is zero just really nothing, a number without any definite or distinct properties?
Even after publication of many papers on the division by zero by different authors, including the authors of this book too, it turned out to be that there is no end in sight of this long lasting and not ending puzzle in mathematics and in science as such. The following book is designed to provide further evidence and to strengthen and to justify our confidence about the possibility of a logically consistent division by zero.