Description
Require safe-integer index from zero through 4096 and return 2^index using exact integers as weightDecimal.
A set contains distinct values, so duplicate input items do not contribute additional members. Ordered output is a serialization convention; membership, equality, and the chosen universe determine the underlying set result.
Require safe-integer index from zero through 4096 and return 2^index using exact integers as weightDecimal.
When to use this tool
Use Set Element Power Weight when you need a deterministic operation on explicitly supplied sets or a finite membership representation.
How to use the tool and how it works
- Enter index. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read weightDecimal. Use the output convention below.
Require safe-integer index from zero through 4096 and return 2^index using exact integers as weightDecimal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| index | Position under the zero-based or one-based convention stated above. | Required. Safe integer; minimum 0; maximum 4096. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| weightDecimal | Weight Decimal | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"index": 7
},
"output": {
"weightDecimal": "128"
}
}Limitations and assumptions
- Index zero has weight one; this is a positional encoding weight, not a complete power set or a numeric floating-point result.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Specify the universe and equality convention before combining this result with other set operations.
References
Similar or alternative tools
- Atom Membership Bit Signature
Read memberships in array order, write true as 1 and false as 0 for signature, and set integer bit i for every true entry.
- Finite Set Cardinality Update
Choose delta +1 or zero for insertion according to alreadyPresent, and -1 or zero for removal.