Read the equation
Two of the operators are identities, one replaces every input by the constant one, and the last takes a reciprocal. The reciprocal requires a nonzero input when used alone. In the displayed sequential chain it receives the constant one, so its potential singularity is removed by the earlier reset.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| f_4 | Identity |
| f_5 | Constant one |
| f_6 | Identity |
| f_7 | Reciprocal |
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
Let f1z=z+1, f2z=z−1, f3z=z. f4z=z, f5z=1, f6z=z, f7z=1/z. Here f4z=z1, f5z=1z, and f6z=z/1. The reciprocal requires a nonzero input. An ordered composite can nevertheless be defined at an initial zero when a preceding operator supplies a nonzero reciprocal input. 6.1 Proposition 1: the sequential loop is a constant map For every finite real initial value in the ordinary interpretation,
Exact original notation
{f}_{4}\left(z\right)=z, {f}_{5}\left(z\right)=1, {f}_{6}\left(z\right)=z, {f}_{7}\left(z\right)=1/z.Sources & provenance
{f}_{4}\left(z\right)=z, {f}_{5}\left(z\right)=1, {f}_{6}\left(z\right)=z, {f}_{7}\left(z\right)=1/z.
{f}_{4}\left(z\right)=z, {f}_{5}\left(z\right)=1, {f}_{6}\left(z\right)=z, {f}_{7}\left(z\right)=1/z.