Difference between revisions of "Limit of Hilger real and imag parts yields classical"

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==Theorem==
<strong>[[Limit of Hilger real and imag parts yields classical|Theorem]]:</strong> The following formula holds:
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The following formula holds:
 
$$\displaystyle\lim_{h \rightarrow 0^+} \left[ \mathrm{Re}_h(z) + \mathring{\iota} \mathrm{Im}_h(z) \right] = \mathrm{Re}(z) + i \mathrm{Im}(z),$$
 
$$\displaystyle\lim_{h \rightarrow 0^+} \left[ \mathrm{Re}_h(z) + \mathring{\iota} \mathrm{Im}_h(z) \right] = \mathrm{Re}(z) + i \mathrm{Im}(z),$$
 
where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$ and $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$.
 
where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$ and $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$.
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<strong>Proof:</strong> █
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==Proof==
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==References==
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[[Category:Theorem]]
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[[Category:Unproven]]

Latest revision as of 12:57, 17 August 2017

Theorem

The following formula holds: $$\displaystyle\lim_{h \rightarrow 0^+} \left[ \mathrm{Re}_h(z) + \mathring{\iota} \mathrm{Im}_h(z) \right] = \mathrm{Re}(z) + i \mathrm{Im}(z),$$ where $\mathrm{Re}_h$ denotes the Hilger real part of $z$ and $\mathrm{Im}_h$ denotes the Hilger imaginary part of $z$.

Proof

References