Difference between revisions of "Hilger real part oplus Hilger imaginary part equals z"

From timescalewiki
Jump to: navigation, search
(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formula holds: $$z = \mathrm{Re}_h(z) \oplus \mathring{\iota} ...")
 
 
(One intermediate revision by the same user not shown)
Line 1: Line 1:
<div class="toccolours mw-collapsible mw-collapsed" style="width:800px">
+
==Theorem==
<strong>Theorem:</strong> The following formula holds:
+
The following formula holds:
$$z = \mathrm{Re}_h(z) \oplus \mathring{\iota} \mathrm{Im}_h(z),$$
+
$$z = \mathrm{Re}_h(z) \oplus_h \mathring{\iota} \mathrm{Im}_h(z),$$
where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$, $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$, and $\mathring{\iota}$ denotes the [[Hilger pure imaginary]].
+
where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$, $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$, $\oplus_h$ denotes the [[circle plus]] operation, and $\mathring{\iota}$ denotes the [[Hilger pure imaginary]].
<div class="mw-collapsible-content">
+
 
<strong>Proof:</strong> █
+
==Proof==
</div>
+
 
</div>
+
==References==
 +
 
 +
[[Category:Theorem]]
 +
[[Category:Unproven]]

Latest revision as of 21:42, 14 July 2016

Theorem

The following formula holds: $$z = \mathrm{Re}_h(z) \oplus_h \mathring{\iota} \mathrm{Im}_h(z),$$ where $\mathrm{Re}_h$ denotes the Hilger real part of $z$, $\mathrm{Im}_h$ denotes the Hilger imaginary part of $z$, $\oplus_h$ denotes the circle plus operation, and $\mathring{\iota}$ denotes the Hilger pure imaginary.

Proof

References