Description
Return member when leftElement occurs in left and rightElement in right, with missingFactors naming absent sides.
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 member when leftElement occurs in left and rightElement in right, with missingFactors naming absent sides.
When to use this tool
Use Cartesian Product Single Pair Membership 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 leftElement, rightElement, left, right. 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 member, missingFactors. Inspect member before interpreting the associated values.
Return member when leftElement occurs in left and rightElement in right, with missingFactors naming absent sides.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftElement | Left Element | Required. Text; maximum UTF-16 length 8192. |
| rightElement | Right Element | Required. Text; maximum UTF-16 length 8192. |
| left | Left | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| right | Right | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| member | Member | Required. Boolean. |
| missingFactors | Missing Factors | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
{
"input": {
"leftElement": "a",
"rightElement": "b",
"left": [
"a"
],
"right": [
"c"
]
},
"output": {
"member": false,
"missingFactors": [
"right"
]
}
}Limitations and assumptions
- This checks one ordered pair without constructing a Cartesian product. Exact strings, not normalized or structured identities, determine membership.
- 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
- Cartesian Product Empty Factor Flag
Multiply nonnegative integer factor sizes using BigInt and return exact decimal size and empty for a zero product.
- Integer Set One Residue Class Membership
Normalize integer modulo positive modulus and return member when the result equals residue, requiring residue from zero through modulus minus one.