Description
Classify sign alternation and an identically zero geometric recurrence from its initial value and ratio.
A sequence rule specifies how terms relate. Checking one transition, advancing a recurrence, and bounding an infinite tail answer different questions. A calculation from supplied coefficients assumes that rule; it does not infer it from observations.
Classify sign alternation and an identically zero geometric recurrence from its initial value and ratio.
When to use this tool
Use it for geometric recurrence sign alternation flag when the required inputs and conventions are already available.
How to use the tool and how it works
- Enter initial, ratio. Use the stated units and boundary conventions.
- Run the calculation. Correct any input error before interpreting a result.
- Read alternates, identicallyZero. Inspect any known, defined, inclusion, or boundary flags before interpreting numeric values.
Report sign alternation when initial is nonzero and ratio is negative, and report identicallyZero when initial is exactly zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| initial | Initial | Required. Finite number. |
| ratio | Dimensionless ratio of compatible quantities under the stated formula. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| alternates | Alternates | Required. Boolean. |
| identicallyZero | Identically Zero | Required. Boolean. |
{
"input": {
"initial": 2,
"ratio": -0.5
},
"output": {
"alternates": true,
"identicallyZero": false
}
}Limitations and assumptions
- A zero ratio with nonzero initial becomes zero after its first step but is not labeled identically zero. This is symbolic recurrence bookkeeping; floating-point underflow in a generated long sequence is not simulated.
- The field tables describe structural bounds; the mechanics also state cross-field requirements. Malformed input shapes, disallowed keys, and invalid domains cause input errors. Results must remain finite and within the declared output contract. A successful false flag or zero placeholder is distinct from an error.
- Numeric arithmetic uses binary floating point. Exact comparisons have no hidden tolerance or decimal rounding; negative zero is exported as zero. Decimal-text integer operations retain the exactness specifically stated above.
Alternative or Complementary methods
For geometric recurrence sign alternation flag, check the source records and the supplied rule before comparing the result with another method. Use exact integer or symbolic arithmetic when a numerical equality is insufficient.
References
Similar or alternative tools
- Affine Recurrence Two Step Constant
Return the coefficients obtained by composing a supplied affine recurrence twice.
- Arithmetic Geometric Single Term Formula
Evaluate one zero-based term of a supplied arithmetic-geometric progression.