Description
Deduplicate both lists, find at most one first-list-only and second-list-only witness, and return equal when neither exists.
A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.
Deduplicate both lists, find at most one first-list-only and second-list-only witness, and return equal when neither exists.
When to use this tool
Use Finite Set Two Witness Equality Status when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.
How to use the tool and how it works
- Enter left, right. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read equal, leftWitness, rightWitness. Inspect equal before interpreting the associated values.
Deduplicate both lists, find at most one first-list-only and second-list-only witness, and return equal when neither exists.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| right | Right | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| equal | Equal | Required. Boolean. |
| leftWitness | Left Witness | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| rightWitness | Right Witness | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
{
"input": {
"left": [
"a",
"b"
],
"right": [
"b",
"c"
]
},
"output": {
"equal": false,
"leftWitness": [
"a"
],
"rightWitness": [
"c"
]
}
}Limitations and assumptions
- Witness lists preserve first-occurrence order and can be empty. Equality is exact string-set equality, not multiplicity, order-sensitive comparison, or normalized real-world identity.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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 full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.
References
Similar or alternative tools
- set/difference
Return unique values from the first string list that are absent from the second.
- Set Equality Single Element Obstruction
Return obstruction when inFirst differs from inSecond and side first, second, or none according to the unmatched membership.