Description
Positive affine transformation preserving the mathematical order; not an interpersonal utility comparison.
A logical calculation operates on a stated representation: truth values, token lists, counts, or an explicitly supplied relation. Checking one assignment, pair, trace, or witness is different from proving a formula or validating an entire argument. Empty domains, duplicate tokens, and scope conventions can change the result.
Positive affine transformation preserving the mathematical order; not an interpersonal utility comparison.
When to use this tool
Use Utility Order Positive Affine Invariance when you need this exact local truth, count, token, relation, or witness check within a larger logic workflow.
How to use the tool and how it works
- Enter first, second, multiplier, offset. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read transformedFirst, transformedSecond, order. Use the output convention below.
For positive multiplier return transformedFirst=multiplier*first+offset, transformedSecond=multiplier*second+offset, and order=sign(first-second).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number. |
| second | Second | Required. Finite number. |
| multiplier | Multiplier | Required. Finite number; strictly above 0. |
| offset | Offset | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| transformedFirst | Transformed First | Required. Finite number. |
| transformedSecond | Transformed Second | Required. Finite number. |
| order | Order | Required. Safe integer. |
{
"input": {
"first": 2,
"second": 3,
"multiplier": 4,
"offset": 10
},
"output": {
"transformedFirst": 18,
"transformedSecond": 22,
"order": -1
}
}Limitations and assumptions
- Order is computed from original utilities rather than recomparing rounded transformed outputs. The algebraic ordering property does not establish an interpersonal or cardinal utility interpretation.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a parser, scope-aware representation, model checker, or proof procedure when the supplied token or witness representation is insufficient. A local passing check should not be promoted to global validity.
References
Similar or alternative tools
- Alpha Equivalence Bound Variable Pair
Compare flat single-binder token bodies, rejecting potential free-variable capture; nested binders are outside this model.
- Argument Assumption Scope Depth
Audit explicit opening/closing assumption-scope actions without evaluating argument validity.