irrational number, n.Definitions

A Irrational number (n.) lives ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠in the substratum of the operations from which it is born.

An Irrational number (n.) is ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠a law, not an infinite decimal extension, since a missing pi would never be felt as a gap.

An Irrational number (n.) has ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠no system or set of higher-order infinity; we only have a method for upsetting any order.

A Irrational number (n.) yields ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠extensions and is not one: an arithmetical law endlessly yielding decimal places.

The Irrational number (n.) are ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠wrongly pictured as spread out along the number line, waiting to be cut into classes.

The Irrational number (n.) admit ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠no series of all of them, just as the row of all books would make no sense if every row of books were itself called a book.