order of factors in infinite product

Theorem.

If the infinite product

$$\prod _{\nu =1}^{\mathrm{\infty }}(1+c_{\nu })=(1+c_1)(1+c_2)\mathrm{\cdots }$$

of complex numbers $1+c_{\nu }$ is absolutely convergent (http://planetmath.org/AbsoluteConvergenceOfInfiniteProduct), then its value, i.e.  $\underset{n\to \mathrm{\infty }}{lim}{\displaystyle \prod _{\nu =1}^n}(1+c_{\nu })$, does not depend on the is zero.