Description
Use coefficient one for odd memberships and minus one for even, returning coefficient*regionCardinality.
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.
Use coefficient one for odd memberships and minus one for even, returning coefficient*regionCardinality.
When to use this tool
Use Set Inclusion Exclusion One Region Term 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 regionCardinality, memberships. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read coefficient, contribution. Use the output convention below.
Use coefficient one for odd memberships and minus one for even, returning coefficient*regionCardinality. Require nonnegative integer cardinality and memberships one through 128.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| regionCardinality | Region Cardinality | Required. Safe integer; minimum 0. |
| memberships | Memberships | Required. Safe integer; minimum 1; maximum 128. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| coefficient | Coefficient | Required. Safe integer. |
| contribution | One term under the stated formula, not necessarily a complete statistic. | Required. Safe integer. |
{
"input": {
"regionCardinality": 5,
"memberships": 2
},
"output": {
"coefficient": -1,
"contribution": -5
}
}Limitations and assumptions
- This is one signed inclusion-exclusion intersection term, not the full union cardinality. The caller must supply compatible intersections and avoid interpreting it as an arbitrary disjoint atom weight.
- 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 Threeway Membership Region Token
Encode inA, inB, and inC as weights four, two, and one and return region plus its three-character ABC token.
- Three Set Venn Region Cardinality Term
Calculate onlyA=a-ab-ac+abc and feasible from its nonnegativity and the supplied pair/triple intersection bounds.