Difference between revisions of "Limit of Hilger real and imag parts yields classical"
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<strong>[[Limit of Hilger real and imag parts yields classical|Theorem]]:</strong> The following formula holds: | <strong>[[Limit of Hilger real and imag parts yields classical|Theorem]]:</strong> 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),$$ |
| + | where $\mathrm{Re}_h$ denotes the [[Hilger real part]] of $z$ and $\mathrm{Im}_h$ denotes the [[Hilger imaginary part]] of $z$. | ||
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<strong>Proof:</strong> █ | <strong>Proof:</strong> █ | ||
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Revision as of 19:54, 29 December 2015
Theorem: The following formula holds: $$\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: █
