Description
Distinguish finite-set membership from subset inclusion using JSON scalar atoms and nested arrays, ignoring set order and duplicate 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.
Distinguish finite-set membership from subset inclusion using JSON scalar atoms and nested arrays, ignoring set order and duplicate elements.
When to use this tool
Use Nested Set Element Versus Subset Label 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 candidateJson, setJson. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read element, subset. Inspect element, subset before interpreting the associated values.
Parse candidateJson and setJson, treating nested arrays as finite sets of typed scalar atoms. Recursively deduplicate and sort member keys for order-insensitive equality, then separately return element membership and subset status for an array candidate.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| candidateJson | Scalar atom or nested arrays representing finite sets. | Required. Text; maximum UTF-16 length 8192. |
| setJson | Bounded outer set as a JSON array; objects rejected. | Required. Text; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| element | Element | Required. Boolean. |
| subset | Subset | Required. Boolean. |
{
"input": {
"candidateJson": "[1]",
"setJson": "[1,2]"
},
"output": {
"element": false,
"subset": true
}
}Limitations and assumptions
- Objects are rejected and bounded input/depth limits apply. Element and subset can both be true; scalar candidates have subset false, while an empty array is a subset without requiring it to be an element.
- 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
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- Set Disjoint Union Tagged Element Key
Parse bounded elementJson and serialize the tuple of tag and that JSON value as key.