Description
Inspect cardinality witnesses for finite-set containment without materializing elements.
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.
Inspect cardinality witnesses for finite-set containment without materializing elements.
When to use this tool
Use Set Containment Slack 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 supersetSize, subsetSize, intersectionSize. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read missingFromSuperset, supersetOnly, contained. Inspect contained before interpreting the associated values.
Return missingFromSuperset=subsetSize-intersectionSize, supersetOnly=supersetSize-intersectionSize, and contained when intersection equals subsetSize. Require feasible nonnegative integer counts.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| supersetSize | Superset Size | Required. Safe integer; minimum 0. |
| subsetSize | Subset Size | Required. Safe integer; minimum 0. |
| intersectionSize | Intersection Size | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| missingFromSuperset | Missing From Superset | Required. Safe integer. |
| supersetOnly | Superset Only | Required. Safe integer. |
| contained | Contained | Required. Boolean. |
{
"input": {
"supersetSize": 10,
"subsetSize": 6,
"intersectionSize": 5
},
"output": {
"missingFromSuperset": 1,
"supersetOnly": 5,
"contained": false
}
}Limitations and assumptions
- Containment is conditional on counts describing actual sets. Empty subsets are contained under this rule, and no elements or matching identities are inspected.
- 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/subset-checker
Set inclusion asks whether every distinct candidate value appears in a supplied superset.
- Subset Counterexample Single Witness
Return counterexample when witness occurs in first and not in second.