Description
Preimage and multiplicity of one supplied target under a finite explicitly tabulated map.
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.
Preimage and multiplicity of one supplied target under a finite explicitly tabulated map.
When to use this tool
Use Set Image Preimage Multiplicity Tag 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 domain, imageValues, target. 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 preimage, multiplicity, inImage. Inspect inImage before interpreting the associated values.
For a distinct domain aligned with imageValues, collect domain elements whose image equals target. Return preimage, multiplicity, and inImage.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| domain | Domain | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| imageValues | Image Values | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| target | Target | Required. Text; maximum UTF-16 length 8192. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| preimage | Preimage | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| multiplicity | Multiplicity | Required. Safe integer. |
| inImage | In Image | Required. Boolean. |
{
"input": {
"domain": [
"a",
"b",
"c"
],
"imageValues": [
"x",
"y",
"x"
],
"target": "x"
},
"output": {
"preimage": [
"a",
"c"
],
"multiplicity": 2,
"inImage": true
}
}Limitations and assumptions
- Multiplicity counts preimage elements rather than duplicate domain rows. The mapping is supplied; function validity beyond the aligned explicit list and target meaning are not inferred.
- 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
- Set Element Canonical Key Type Tag
Parse valueJson as a bounded JSON scalar and return a key consisting of its type tag and JSON serialization, treating null with its own tag.
- Bounded Set Cardinality Uncertainty Pair
Deduplicate definite and possible members, require definite to be a subset of possible, and return minimum and maximum cardinalities.