@user170039 - His first definition (2.1.1) contains such undefined symbols as {, }, 1, 2, 3, 4, ... and set which was defined later in 3.11. He mentioned an alternative definition of number by means of cardinality, whose definition in 3.6.5 is not independent from the one defined in 2.1.1. Also he uses Peano's axioms which can be about bricks or telephone poles, not necessarily numbers. Mathematical Induction (axiom 2.5 ) is given as an axiom, which is antediluvian.

This book could have deserved a passing grade if each of his definitions and axioms is independent or strictly constructed on previous definitions or axioms, which is clearly not the case.