Description
Map a real interval through absolute value.
Distances between intervals and bounds on metric distances describe geometric separation under declared assumptions. Touching intervals have zero gap; triangle bounds require distances that share a common endpoint in an actual metric.
Map a real interval through absolute value.
When to use this tool
Use Distance Interval Absolute Value Envelope when checking a supplied interval gap or metric distance bound.
How to use the tool and how it works
- Enter lower, upper. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read minimum, maximum. Use the output convention below.
Map a real interval through absolute value. Require lower <= upper; minimum is zero if the interval contains zero, otherwise the smaller endpoint magnitude; maximum is the larger magnitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| minimum | Minimum | Required. Finite number. |
| maximum | Maximum | Required. Finite number. |
{
"input": {
"lower": -2,
"upper": 3
},
"output": {
"minimum": 0,
"maximum": 3
}
}Limitations and assumptions
- These are deterministic endpoint bounds, not statistical confidence limits.
- 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
Use the full point or set geometry and a suitable metric when you need an actual distance rather than a bound or local term.
References
Similar or alternative tools
- Distance: Point To Open Interval Distance
Return distance infimum to an open interval and whether it is attained.
- Chebyshev Interval Uncertainty Gap
Return minimum Chebyshev gap between axis-aligned boxes.