Description
Encode inA, inB, and inC as weights four, two, and one and return region plus its three-character ABC token.
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.
Encode inA, inB, and inC as weights four, two, and one and return region plus its three-character ABC token.
When to use this tool
Use Set Threeway Membership Region Token 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 inA, inB, inC. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read region, token. Use the output convention below.
Encode inA, inB, and inC as weights four, two, and one and return region plus its three-character ABC token.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| inA | In A | Required. Boolean. |
| inB | In B | Required. Boolean. |
| inC | In C | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| region | ABC membership encoded with weights four, two, and one. | Required. Safe integer. |
| token | Token | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"inA": true,
"inB": false,
"inC": true
},
"output": {
"region": 5,
"token": "101"
}
}Limitations and assumptions
- A is the most significant bit in this convention. This identifies one membership region without constructing a Venn diagram, inferring its size, or verifying elements.
- 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 Single Pair Membership
Return member when leftElement occurs in left and rightElement in right, with missingFactors naming absent sides.
- 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.