Hilger real part
From timescalewiki
Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger real part of $z$ is defined by $$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$
Properties
Inequality for Hilger real part
Limit of Hilger real and imag parts yields classical
Hilger real part oplus Hilger imaginary part equals z
