The elements of the true arithmetic of infinities

I am fully convinced that the ideas in this book are based on clear and certain principles and will survive the most intense criticism. However, based on how my previous work has been treated by critics, I expect to face heavy misrepresentation and harsh insults. I anticipate whatever hatred and envy can produce, or whatever tricks a dishonest person can use to twist the truth. My only goal is to spread the highest kind of truth and to help my fellow countrymen and all people in a significant way. Because of this, I comfort myself against any insults I have received or may yet receive. I know my intentions are honest, and I have a firm hope that what I have written for the benefit of others will be approved by the wise and the good. I learned long ago from the school of Pythagoras that the praise or the blame of a foolish person are both equally ridiculous.
original Greek: Ηγου παντος ανοητου και τον επαινον και τον ψογον καταγελαστον.

Some people may object to my use of the phrase the last term of an infinite series. They might see it as a contradiction or a total solecism a grammatical or logical error. I must explain that this phrase simply refers to the specific term in an infinite series which is the greatest for whole numbers, or the least for fractions, that can possibly exist in that series. This greatest or least term can only be described