Difference between revisions of "Hilger real part"
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Revision as of 15:46, 22 September 2016
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
Theorem: The following inequality holds for $z \in \mathbb{C}_h$: $$-\dfrac{1}{h} < \mathrm{Re}_h(z) < \infty.$$
Proof: █
Limit of Hilger real and imag parts yields classical
Hilger real part oplus Hilger imaginary part equals z
