Difference between revisions of "Hilger real part oplus Hilger imaginary part equals z"
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(Created page with "<div class="toccolours mw-collapsible mw-collapsed" style="width:800px"> <strong>Theorem:</strong> The following formula holds: $$z = \mathrm{Re}_h(z) \oplus \mathring{\iota} ...") |
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− | + | ==Theorem== | |
− | + | The following formula holds: | |
− | $$z = \mathrm{Re}_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]]. |
− | + | ||
− | + | ==Proof== | |
− | + | ||
− | + | ==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.