Under the usual real order, a=-13, b=-26, and c=-1. Compare a+c and b+c, giving <, =, or > in that order.
G001 — Under the usual real order, a=-13, b=-26, and c=-1. Compare a+c and b+c, giving <, =, or > in that order.
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.
Check THIS bank’s keys/operation/domain:legacy table underscores,MOD50 local hyphens;permissive BASE data acquires no unknown-field restriction.Keep Number.isInteger and SAFE source guards distinct,while preserving ORIGINAL JSON number representations.
Translation ORIGINAL a plus same c := sum(-13, -1)
After
Translation ORIGINAL a plus same c = -14
Conditions: none
Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.
Translation ORIGINAL b plus same c := sum(-26, -1)
After
Translation ORIGINAL b plus same c = -27
Conditions: none
Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.
Translation ORIGINAL translated left minus right := sub(-14, -27)
After
Translation ORIGINAL translated left minus right = 13
Conditions: none
Calculate exactly from ORIGINAL ordered operands.Legacy derived integers are not recapped at the RAW SAFE bound;MOD50 rationals separately retain the NAIVE pre-reduction source envelope.
Adding the SAME c to BOTH sides preserves difference a−b.Subtract c from both to recover the original comparison,including equality and negative c.Never translate only one side;derived sums may exceed SAFE.
S005 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
S004 · premise_and_result_audit — Recompute Translation ORIGINAL translated left minus right with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Translation ORIGINAL b plus same c with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute Translation ORIGINAL a plus same c with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — Reverse-audit THIS step against the ORIGINAL roles,complete premises and field order.Distinguish implication from equivalence;preserve originals,English,MKOs,ASTs and review states.Finite checks are not independent review or general formal proof.
Result
>
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.