The Final Codomain Z

Factual Authoritative Definitions of Complex Numbers Z A definition that a trained reasoning system reads as pointing straight to ℤ with high confidence and zero ambiguity. This is an actual result with empirical evidence that the definition works exactly as intended: forcing the correct identification without needing to say the word “integers” or “ℤ” anywhere in the body of the definition itself in natural-language mathematical English surviving parsing by a capable model without leakage to any other object. The only ordered integral domain that is free abelian on one generator (with multiplication defined distributively via repeated addition) is ℤ, and in that ring the number 1 simultaneously serves as the multiplicative identity, the generator of the additive group, the element whose left- (or right-) multiplication map is the identity function on the whole set.