Description
Require element and every members entry inside the supplied universe, then return member and its boolean complement.
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.
Require element and every members entry inside the supplied universe, then return member and its boolean complement.
When to use this tool
Use Set Membership Negation Universe Guard 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, universe. 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 member, complement. Inspect member, complement before interpreting the associated values.
Require element and every members entry inside the supplied universe, then return member and its boolean complement.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. |
| universe | Universe | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| member | Member | Required. Boolean. |
| complement | Complement | Required. Boolean. |
{
"input": {
"element": "b",
"members": [
"a"
],
"universe": [
"a",
"b"
]
},
"output": {
"member": false,
"complement": true
}
}Limitations and assumptions
- An outside-universe query is an error, not a complemented member. No universe is inferred, duplicates have no effect, and equality is exact string equality.
- 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 Membership Unknown Universe Code
Require subset members inside universe, then label element outside-universe, member, or nonmember.
- Cartesian Product Single Pair Membership
Return member when leftElement occurs in left and rightElement in right, with missingFactors naming absent sides.