Difference between revisions of "Hilger complex plane"

From timescalewiki
Jump to: navigation, search
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
 
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 $\mathbb{C}_0=\mathbb{C}$.
  
Line 10: Line 10:
  
 
[[Category:Definition]]
 
[[Category:Definition]]
 +
 +
<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