I am completely lost. I understand how field axioms and Natural, Integers, Rational numbers relate to Field Axioms. However, I dont understand how irrational number R/Q relate to all of them. What Field Axioms A1-A5, M1-M5, and DL relate to Irrational Numbers R/Q? Furthermore, how does R/Q relate to Well-ordering propery, Completeness Axiom, Denumerable, Uncountable, and Density in the Reals?