Question 29624: Coordinate Addition in a Fixed Real Space

Original question and givens

Use a fixed real coordinate space with nonempty vectors of the same dimension; integer coordinates and scalars are special real instances. Check only the declared coordinate instance, not all abstract vector-space axioms for an arbitrary structure. left=[11, -1, -21], right=[1, 15, 2]. Give (left,right,the componentwise sum).

• G001 — Use a fixed real coordinate space with nonempty vectors of the same dimension; integer coordinates and scalars are special real instances. Check only the declared coordinate instance, not all abstract vector-space axioms for an arbitrary structure. left=[11, -1, -21], right=[1, 15, 2]. Give (left,right,the componentwise sum).

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-real-vector-space

Step-by-step derivation

source roles = [qf-str22-vectorspace-addition, vectorspace-addition]

derived = [[left, right, result]]

Vector ORIGINAL addition coordinate0 := sum(11, 1)

Vector ORIGINAL addition coordinate0 = 12

Vector ORIGINAL addition coordinate1 := sum(-1, 15)

Vector ORIGINAL addition coordinate1 = 14

Vector ORIGINAL addition coordinate2 := sum(-21, 2)

Vector ORIGINAL addition coordinate2 = -19

source roles = [[11, -1, -21], [1, 15, 2]]

derived = [[12, 14, -19]]

Reverse checks

• S005 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.
• S004 · premise_and_result_audit — Recompute Vector ORIGINAL addition coordinate2 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute Vector ORIGINAL addition coordinate1 with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute Vector ORIGINAL addition coordinate0 with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Reverse-check EACH original datum,index,direction,representative and premise,not only the answer.Exact candidate checking,independent review,formal proof and publication clearance remain separate.

Result

([11, -1, -21], [1, 15, 2], [12, 14, -19])

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.