Manuscript XVI-J@1 · XVI-J.tex · proposition · 6c1f306d

Proposition: Changing the subtraction function

An operational extension prescription › The selected extension · lines 1274–1289 · proof included or linked

XVI-J@1#prop:changevarpi, XVI-J@1#eq:changevarpi

For two allowed functions $ϖ_{1}, ϖ_{2}$ ,

q ˉ^{R_{ϖ_{2}}} - q ˉ^{R_{ϖ_{1}}} = T_{0} (ϖ_{1} - ϖ_{2}) δ .

Proof. Their difference vanishes at zero. Subtracting the two instances of (eq:extension) proves the identity on every test.

Displayed formulas in this passage

XVI-J@1#eq:changevarpi · line 1277
$q ˉ^{R_{ϖ_{2}}} - q ˉ^{R_{ϖ_{1}}} = T_{0} (ϖ_{1} - ϖ_{2}) δ .$