Description
Return witness when the supplied element occurs in both left and right.
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.
Return witness when the supplied element occurs in both left and right.
When to use this tool
Use Set Pair Disjointness Single Element 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, 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 witness. Inspect witness before interpreting the associated values.
Return witness when the supplied element occurs in both left and right.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| element | Element | Required. Text; maximum UTF-16 length 8192. |
| 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 |
|---|---|---|
| witness | Witness | Required. Boolean. |
{
"input": {
"element": "b",
"left": [
"a",
"b"
],
"right": [
"b",
"c"
]
},
"output": {
"witness": true
}
}Limitations and assumptions
- A false result does not prove disjointness because other elements may overlap. This checks one candidate witness without returning a complete intersection.
- 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 Partition Block Disjointness Pair
Return distinct shared witnesses in first-list order and disjoint when that witness list is empty.
- set/intersection
Return unique strings shared by two lists.