Difference between revisions of "Hilger real part"
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(Created page with "Let $h>0$ and let $z \in \mathbb{C}_h$, the Hilger complex plane. The Hilger real part of $z$ is defined by $$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$") |
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Let $h>0$ and let $z \in \mathbb{C}_h$, the [[Hilger complex plane]]. The Hilger real part of $z$ is defined by | Let $h>0$ and let $z \in \mathbb{C}_h$, the [[Hilger complex plane]]. The Hilger real part of $z$ is defined by | ||
$$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$ | $$\mathrm{Re}_h(z)=\dfrac{|zh+1|-1}{h}.$$ | ||
| + | |||
| + | =Properties= | ||
| + | <div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> | ||
| + | <strong>Theorem:</strong> The following inequality holds for $z \in \mathbb{C}_h$: | ||
| + | $$-\dfrac{1}{h} < \mathrm{Re}_h(z) < \infty.$$ | ||
| + | <div class="mw-collapsible-content"> | ||
| + | <strong>Proof:</strong> █ | ||
| + | </div> | ||
| + | </div> | ||
Revision as of 19:51, 29 December 2015
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: █
