Concept guide
Integer: deciding membership, the meaning of the minus sign, and closure under negation
Inside the reals, take Z={0}∪N⁺∪{−n ∣ n∈N⁺} (N contains 0 by the OCME convention, N⁺=N∖{0}, and −n is the additive inverse of n). Prove −7∈Z; show that the decimal numeral '3.0' denotes the integer 3; prove −2.5∉Z; prove −(−a)=a from uniqueness of additive inverses, in particular −(−4)=4; prove −z∈Z for every z∈Z; and use 5−8=5+(−8)=−3 to tell binary subtraction from the unary minus sign.