Description
Test value against ordered lower and upper bounds with independently selected lowerClosed and upperClosed flags.
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.
Test value against ordered lower and upper bounds with independently selected lowerClosed and upperClosed flags.
When to use this tool
Use Set Interval Boundary Member Policy 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 value, lower, upper, lowerClosed, upperClosed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read member. Inspect member before interpreting the associated values.
Test value against ordered lower and upper bounds with independently selected lowerClosed and upperClosed flags.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| lowerClosed | Lower Closed | Required. Boolean. |
| upperClosed | Upper Closed | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| member | Member | Required. Boolean. |
{
"input": {
"value": 2,
"lower": 2,
"upper": 5,
"lowerClosed": true,
"upperClosed": false
},
"output": {
"member": true
}
}Limitations and assumptions
- For equal endpoints only both closed can admit that value. This is one finite numeric interval check without tolerance, unions, infinity endpoints, or an inferred boundary convention.
- 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
- Interval Set Touching Endpoint Policy
For positive-length ordered intervals with firstUpper<=secondLower, return touches at equality and intersectsAtJoin only when both facing endpoint flags are closed.
- Interval Touch Point Isolated Flag
Touch behavior of two ordered nonoverlapping interval interiors with explicit adjacent endpoint closure.