Description
Return complement=inUniverse&&!inSet and valid=inUniverse||!inSet.
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 complement=inUniverse&&!inSet and valid=inUniverse||!inSet.
When to use this tool
Use Set Complement Explicit Universe Boundary 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 inUniverse, inSet. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read complement, valid. Inspect complement, valid before interpreting the associated values.
Return complement=inUniverse&&!inSet and valid=inUniverse||!inSet.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inUniverse | In Universe | Required. Boolean. |
| inSet | In Set | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| complement | Complement | Required. Boolean. |
| valid | Whether this tool’s specific rule passes, not a broader approval. | Required. Boolean. |
{
"input": {
"inUniverse": false,
"inSet": true
},
"output": {
"complement": false,
"valid": false
}
}Limitations and assumptions
- The only invalid assignment is membership in the set but not its declared universe. Invalid flags are reported rather than rejected, and no actual universe or element list is checked.
- 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
- Finite Set Complement Cardinality Pair
Deduplicate universe and members, require members inside the universe, and return complement in universe order plus memberCount and complementCount.
- Power Set Member Complement Index
Build an elements-bit mask and XOR it with exact decimal index for complementIndex.