# Difference between revisions of "Hilger real part"

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− | + | [[Limit of Hilger real and imag parts yields classical]]<br /> | |

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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