Question 4822: Natural Closed-Interval Cardinality

Original question and givens

N includes 0. lo=0, hi=20. Find |{n∈N: lo≤n≤hi}|, including endpoints.

• G001 — N includes 0. lo=0, hi=20. Find |{n∈N: lo≤n≤hi}|, including endpoints.

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

inclusive interval endpoint difference := sub(20, 0)

inclusive interval endpoint difference = 20

inclusive natural interval size := sum(20, 1)

inclusive natural interval size = 21

lo=0;hi=20

natural interval size=21

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 — Recompute inclusive natural interval size with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute inclusive interval endpoint difference with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

21

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.