Description
Count union membership from explicit member/family incidences, ignoring duplicate incidences.
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.
Count union membership from explicit member/family incidences, ignoring duplicate incidences.
When to use this tool
Use Family Union Support Count 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 members, familyLabels. 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 unionCount, familyCount, repeatedMemberships. Use the output convention below.
Group aligned members by distinct familyLabels. Return unionCount, distinct familyCount, and repeatedMemberships as each member's distinct-family count minus one, summed.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| members | Members | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| familyLabels | Family Labels | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| unionCount | Union Count | Required. Safe integer. |
| familyCount | Family Count | Required. Safe integer. |
| repeatedMemberships | Repeated Memberships | Required. Safe integer. |
{
"input": {
"members": [
"a",
"a",
"b"
],
"familyLabels": [
"X",
"Y",
"Y"
]
},
"output": {
"unionCount": 2,
"familyCount": 2,
"repeatedMemberships": 1
}
}Limitations and assumptions
- Repeated identical member/family pairs do not increase the total. FamilyCount covers only labels appearing in rows, so empty unlisted family sets are not represented.
- 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 Prefix Cover Count Gap
Deduplicate universe and return members absent from covered as missing, with gap equal to that missing count.
- Multiset Count Map Negative Entry Flag
For distinct keys aligned with signed integer counts, list negativeKeys and return valid when that list is empty.