Question 4860: Exact Rational Candidates for N

Original question and givens

N includes 0. Ordered rational candidates=[9/1, -9/1, 10/19]. Give the Yes/No membership list for N.

• G001 — N includes 0. Ordered rational candidates=[9/1, -9/1, 10/19]. Give the Yes/No membership list for N.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-natural-number

Step-by-step derivation

N={0,1,2,...}

0 belongs;negative and nonintegral rational values do not

raw rational=[9, 1];reduced=9/1

nonnegative integer=Yes

raw rational=[-9, 1];reduced=-9/1

nonnegative integer=No

raw rational=[10, 19];reduced=10/19

nonnegative integer=No

Reverse checks

• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

[Yes, No, No]

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.