Difference between revisions of "Hilger real part oplus Hilger imaginary part equals z"
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| − | <strong>Theorem:</strong> The following formula holds: | + | <strong>[[Hilger real part oplus Hilger imaginary part equals z|Theorem]]:</strong> The following formula holds: |
| − | $$z = \mathrm{Re}_h(z) \ | + | $$z = \mathrm{Re}_h(z) \oplus_h \mathring{\iota} \mathrm{Im}_h(z),$$ |
| − | where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$, $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$, and $\mathring{\iota}$ denotes the [[Hilger pure imaginary]]. | + | where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$, $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$, $\oplus_h$ denotes the [[circle plus]] operation, and $\mathring{\iota}$ denotes the [[Hilger pure imaginary]]. |
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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Revision as of 20:01, 29 December 2015
Theorem: The following formula holds: $$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: █
