Read the equation
The interval begins at 1/5 and extends to values below one. On it, the factorization of F(z)−1 keeps the next state at or below one, while F(z)−z is positive. It is an interval for a specific mathematical argument, not a model performance band.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| z | Current state |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
Two factorizations establish the result: Fz−z=1−z2z+17z, Fz−1=5z−1z−17z. For z>1, these show 1<Fz<z. The sequence decreases while bounded below by one. For 1/5≤z<1, they show z<Fz≤1, so the sequence increases while bounded above by one. For 0<z<1/5, the next value is greater than one and thereafter belongs to the first case. A bounded monotone sequence has a limit; continuity and the positive fixed-point equation force that limit to be one. For z0=2, local computation gives: Iteration State
Exact original notation
1/5\le z<1