Description
Touch behavior of two ordered nonoverlapping interval interiors with explicit adjacent endpoint closure.
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.
Touch behavior of two ordered nonoverlapping interval interiors with explicit adjacent endpoint closure.
When to use this tool
Use Interval Touch Point Isolated Flag 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 firstLower, firstUpper, secondLower, secondUpper, firstEndClosed, secondStartClosed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read touch, intersectionIsPoint, connectedUnion. Inspect touch, intersectionIsPoint, connectedUnion before interpreting the associated values.
For ordered nonoverlapping numeric intervals, flag touch at firstUpper==secondLower. At a touch return intersectionIsPoint only when both facing ends are closed and connectedUnion when either facing end is closed.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstLower | First Lower | Required. Finite number. |
| firstUpper | First Upper | Required. Finite number. |
| secondLower | Second Lower | Required. Finite number. |
| secondUpper | Second Upper | Required. Finite number. |
| firstEndClosed | First End Closed | Required. Boolean. |
| secondStartClosed | Second Start Closed | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| touch | Touch | Required. Boolean. |
| intersectionIsPoint | Intersection Is Point | Required. Boolean. |
| connectedUnion | Local touching-endpoint rule; does not validate missing endpoint conditions. | Required. Boolean. |
{
"input": {
"firstLower": 0,
"firstUpper": 1,
"secondLower": 1,
"secondUpper": 2,
"firstEndClosed": true,
"secondStartClosed": false
},
"output": {
"touch": true,
"intersectionIsPoint": false,
"connectedUnion": true
}
}Limitations and assumptions
- Only facing endpoint flags are supplied. Degenerate intervals' other endpoint conditions are not represented, so these local join flags do not validate a complete interval-set representation.
- 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.
- Set Interval Boundary Member Policy
Test value against ordered lower and upper bounds with independently selected lowerClosed and upperClosed flags.