Description
Deduplicate definite and possible members, require definite to be a subset of possible, and return minimum and maximum cardinalities.
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.
Deduplicate definite and possible members, require definite to be a subset of possible, and return minimum and maximum cardinalities.
When to use this tool
Use Bounded Set Cardinality Uncertainty Pair 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 definite, possible. 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 minimum, maximum. Use the output convention below.
Deduplicate definite and possible members, require definite to be a subset of possible, and return minimum and maximum cardinalities.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| definite | Definite | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| possible | Possible | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minimum | Distinct definite-member count. | Required. Safe integer. |
| maximum | Distinct possible-member count. | Required. Safe integer. |
{
"input": {
"definite": [
"a"
],
"possible": [
"a",
"b",
"b"
]
},
"output": {
"minimum": 1,
"maximum": 2
}
}Limitations and assumptions
- These are deterministic count bounds under supplied membership uncertainty, not probabilities or confidence limits. The possible and definite classifications are not independently verified.
- 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 Union One Element Cardinality Delta
Return delta zero for alreadyMember or one otherwise and add it to nonnegative integer cardinality.