Question 1494: Equal Dimension Vectors Are Not a Physical Proof

Original question and givens

Use basic dimension exponent vectors [L,M,T] in that order. Input exponents and the integer power are bounded, but a computed result need not stay inside the input bound. Dimension agreement is necessary but not sufficient for physical correctness; unit scale conversions are separate. left=[1, 1, -2], right=[2, 1, -2]. Give (left vector, right vector, identical?).

• G001 — Use basic dimension exponent vectors [L,M,T] in that order. Input exponents and the integer power are bounded, but a computed result need not stay inside the input bound. Dimension agreement is necessary but not sufficient for physical correctness; unit scale conversions are separate. left=[1, 1, -2], right=[2, 1, -2]. Give (left vector, right vector, identical?).

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-dimensional-analysis

Step-by-step derivation

dimension coordinate order=[L,M,T]

left/base=[1, 1, -2]; right=[2, 1, -2]

L exponent difference := sub(1, 2)

L exponent difference = -1

M exponent difference := sub(1, 1)

M exponent difference = 0

T exponent difference := sub(-2, -2)

T exponent difference = 0

[No, Yes, Yes]

dimensionally consistent: No

Reverse checks

• S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S004 · premise_and_result_audit — Recompute T exponent difference with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute M exponent difference with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute L exponent 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

([1, 1, -2], [2, 1, -2], 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.