Difference between revisions of "Hilger complex plane"

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Let $h>0$ be fixed. We define the Hilger complex plane to be
 
Let $h>0$ be fixed. We define the Hilger complex plane to be
−
$$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq \dfrac{1}{h} \right\},$$
+
$$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq -\dfrac{1}{h} \right\},$$
 
and for $h=0$, we let $\mathbb{C}_0=\mathbb{C}$.
 
and for $h=0$, we let $\mathbb{C}_0=\mathbb{C}$.
  
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[[Category:Definition]]
 
[[Category:Definition]]
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<center>{{:Hilger complex plane footer}}</center>

Latest revision as of 12:45, 6 June 2023

Let $h>0$ be fixed. We define the Hilger complex plane to be $$\mathbb{C}_h = \left\{ z \in \mathbb{C} \colon z \neq -\dfrac{1}{h} \right\},$$ and for $h=0$, we let $\mathbb{C}_0=\mathbb{C}$.

Properties

References

Hilger complex plane and friends

$\Huge\mathbb{A}_h$
Hilger alternating axis
$\Huge\mathbb{I}_h$
Hilger circle
$\Huge\mathbb{C}_h$
Hilger complex plane
$\Huge\mathrm{Im}_h$
Hilger imaginary part
$\Huge\mathring{\iota}$
Hilger pure imaginary
$\Huge\mathbb{R}_h$
Hilger real axis
$\Huge\mathrm{Re}_h$
Hilger real part
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