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finite_product_of_complex_numbers [2014/03/21 11:11] 127.0.0.1 external edit |
finite_product_of_complex_numbers [2015/04/28 14:35] nikolaj |
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| ===== Finite product of complex numbers ===== | ===== Finite product of complex numbers ===== | ||
| - | ==== Set ==== | + | ==== Function ==== |
| - | | @#55CCEE: context | @#55CCEE: $ (z_i) \in \mathrm{FinSequence}(\mathbb C)$ | | + | | @#FF9944: definition | @#FF9944: it $\equiv$ Finite sum over a monoid w.r.t $\langle\!\langle {\mathbb C},\cdot \rangle\!\rangle$ | |
| - | | @#55CCEE: context | @#55CCEE: $ n = \mathrm{length}((z_i)) $ | | + | |
| - | | @#FFBB00: definiendum | @#FFBB00: $\prod: \mathrm{FinSequence}(\mathbb C)\to \mathbb C$ | | + | ----- |
| - | | @#FFBB00: definiendum | @#FFBB00: $\prod_{i=1}^n\ z_i:= \begin{cases} 1 & \mathrm{if}\ n=0\\\\ \left(\prod_{i=1}^{n-1}\ z_i\right)\ \cdot\ z_n & \mathrm{else} \end{cases}$ | | + | $\prod_{k=1}^n\left(1+\frac{1}{k}\right)=n+1$ |
| - | + | ----- | |
| - | ==== Discussion ==== | + | |
| - | ==== Parents ==== | + | |
| === Subset of === | === Subset of === | ||
| [[Finite sum over a monoid]] | [[Finite sum over a monoid]] | ||
| + | === Requirements === | ||
| + | [[Complex number]] | ||
