Infinite product of negative numbers? $-1\times -1\times-1\times -1\dots=$

Question

Edited: Making the question as brief as possible to avoid future confusion and misunderstanding.

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Note

This was moved as a separate question from: Product of all real numbers in a given interval $[n,m]$

Since it was a part of it that wasn't getting any attention.

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Question

How would one calculate the infinite product of negative numbers? For example, in this case:

$$-1\times -1\times-1\times -1\dots=$$

Or is the result of this series simply undefined?

Answer 1

How would one calculate, or attach a value to the infinite product of negative numbers?

For example, in this case: $(-1)\times(-1)\times(-1)\times(-1)\ldots=$?

The value of $\lim\limits_{n\to\infty}(-1)^n$ is undefined.

Answer 2

You could attach some the value of a limit of the average of the values if such a limit of averages would converge. For example arithmetic average of +1-1+1-1... would be 0 as when dividing by the number n of terms so far the oscillations would get below any $\epsilon\in \mathbb{R}$.