Description
Audit one proposed partition block for unique coverage, outside elements and repeated entries.
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.
Audit one proposed partition block for unique coverage, outside elements and repeated entries.
When to use this tool
Use Set Partition One Block Coverage Budget 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 universe, block. 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 covered, outside, duplicates, remaining. Use the output convention below.
Deduplicate block, compare it with a distinct universe, and return covered count, outside elements, duplicate occurrence count, and remaining universe size.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| universe | Universe | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| block | Block | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| covered | Covered | Required. Safe integer. |
| outside | Outside | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| duplicates | Duplicates | Required. Safe integer. |
| remaining | Remaining | Required. Safe integer. |
{
"input": {
"universe": [
"a",
"b",
"c"
],
"block": [
"a",
"a",
"x"
]
},
"output": {
"covered": 1,
"outside": [
"x"
],
"duplicates": 1,
"remaining": 2
}
}Limitations and assumptions
- Outside elements are reported rather than rejected. This audits one proposed block, without checking other blocks, pairwise disjointness, or a complete partition.
- 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
- Partition Block Count Change
Compare declared partition block counts without constructing or validating the partitions.
- Partition Block Size Residual
Check cardinality balance of supplied partition block sizes without claiming their disjointness.