Difference between revisions of "Forward circle minus"
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Revision as of 20:04, 29 December 2015
Let $h>0$ and $z_1,z_2 \in \mathbb{C}_h$, the Hilger complex plane. We define the $\ominus_h$ operation by $$\ominus_h z = \dfrac{-z}{1+zh}.$$
Properties
Theorem: The circle minus $\ominus_h$ is the inverse operation of the circle plus operation $\oplus_h$. Moreover, $$z \ominus_h w = z \oplus_h (\ominus_h w).$$
Proof: █
