Description
Build an elements-bit mask and XOR it with exact decimal index for complementIndex.
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.
Build an elements-bit mask and XOR it with exact decimal index for complementIndex.
When to use this tool
Use Power Set Member Complement Index 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 index, elements. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read complementIndex. Use the output convention below.
Build an elements-bit mask and XOR it with exact decimal index for complementIndex. Require integer elements zero through 128 and index within zero and 2^elements-1.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| index | Exact decimal bitmask index under the supplied elements-bit convention. | Required. Text; maximum UTF-16 length 8192. |
| elements | Elements | Required. Safe integer; minimum 0; maximum 128. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| complementIndex | Complement Index | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"index": "5",
"elements": 4
},
"output": {
"complementIndex": "10"
}
}Limitations and assumptions
- The caller defines the ground-set bit order. Zero elements permits index zero only; no element list, power-set enumeration, or cultural numbering convention is inferred.
- 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.
- Set Complement Explicit Universe Boundary
Return complement=inUniverse&&!inSet and valid=inUniverse||!inSet.