Description
Return delta zero for alreadyMember or one otherwise and add it to nonnegative integer cardinality.
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.
Return delta zero for alreadyMember or one otherwise and add it to nonnegative integer cardinality.
When to use this tool
Use Set Union One Element Cardinality Delta 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 cardinality, alreadyMember. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read cardinality, delta. Use the output convention below.
Return delta zero for alreadyMember or one otherwise and add it to nonnegative integer cardinality. Reject alreadyMember true for an empty set count.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cardinality | Cardinality | Required. Safe integer; minimum 0. |
| alreadyMember | Already Member | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| cardinality | Cardinality | Required. Safe integer. |
| delta | Delta | Required. Safe integer. |
{
"input": {
"cardinality": 5,
"alreadyMember": false
},
"output": {
"cardinality": 6,
"delta": 1
}
}Limitations and assumptions
- The membership flag and count are supplied and no actual set is inspected or changed. Output safe-integer limits still apply when adding to the largest permitted count.
- 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 Disjoint Union Tagged Element Key
Parse bounded elementJson and serialize the tuple of tag and that JSON value as key.
- Bounded Set Cardinality Uncertainty Pair
Deduplicate definite and possible members, require definite to be a subset of possible, and return minimum and maximum cardinalities.