Description
Return newRank=oldRank+1 only when the element was not already present and insertedRank<=oldRank.
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 newRank=oldRank+1 only when the element was not already present and insertedRank<=oldRank.
When to use this tool
Use Finite Set Rank After One Insertion 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 oldRank, insertedRank, alreadyPresent. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read newRank. Use the output convention below.
Return newRank=oldRank+1 only when the element was not already present and insertedRank<=oldRank. Require nonnegative integer ranks.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| oldRank | Old Rank | Required. Safe integer; minimum 0. |
| insertedRank | Inserted Rank | Required. Safe integer; minimum 0. |
| alreadyPresent | Already Present | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| newRank | New Rank | Required. Safe integer. |
{
"input": {
"oldRank": 3,
"insertedRank": 2,
"alreadyPresent": false
},
"output": {
"newRank": 4
}
}Limitations and assumptions
- The ranks are supplied without a list or maximum size. This models one insertion's index shift rather than verifying membership, locating an insertion, or updating an ordered set.
- 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
- Ordered Set Neighbor Insertion Rank
Locate a new value in a strictly increasing numeric sorted list and return zero-based insertion rank, predecessor, successor, and presence flags.
- Finite Set Complement Cardinality Pair
Deduplicate universe and members, require members inside the universe, and return complement in universe order plus memberCount and complementCount.