Description
Test exact element membership in members and return subset for the corresponding singleton, plus missing empty or containing that element.
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.
Test exact element membership in members and return subset for the corresponding singleton, plus missing empty or containing that element.
When to use this tool
Use Set Singleton Subset Witness 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 element, members. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read subset, missing. Inspect subset before interpreting the associated values.
Test exact element membership in members and return subset for the corresponding singleton, plus missing empty or containing that element.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| element | Element | Required. Text; maximum UTF-16 length 8192. |
| members | Members | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| subset | Subset | Required. Boolean. |
| missing | Missing | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
{
"input": {
"element": "b",
"members": [
"a"
]
},
"output": {
"subset": false,
"missing": [
"b"
]
}
}Limitations and assumptions
- Only the singleton subset relation is tested. Duplicates do not change membership, and no broader set inclusion, element normalization, or actual record identity is established.
- 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
- Subset Counterexample Single Witness
Return counterexample when witness occurs in first and not in second.
- Finite Set Two Witness Equality Status
Deduplicate both lists, find at most one first-list-only and second-list-only witness, and return equal when neither exists.