I am afraid, that multiplication of even countably many small numbers yields 0. Let alone the product of more than that, what your integration analogous operation would be,
You can get a nonzero product if the sum of differences between 1 and your factors converge. Then and only then. But if all the factors are smaller than say 0.9 … you get 0.
Except if you can find some creative way to that anyway. Might be possible, I don’t know.
Yeah, it might have helped to clarify that the infinitesimal factors I had in mind are not infinitely small as numbers from the standpoint of addition. Since the factor that makes no change to the product is 1 rather than 0, “infinitely small” factors must be infinitesimally greater than 1, not 0. In particular, I was talking about a Type II product integral with the formula pi(1 + f(x).dx). If f(x) = 1, then we get e^sigma(1.dx) = e^constant = constant, right?
I am afraid, that multiplication of even countably many small numbers yields 0. Let alone the product of more than that, what your integration analogous operation would be,
You can get a nonzero product if the sum of differences between 1 and your factors converge. Then and only then. But if all the factors are smaller than say 0.9 … you get 0.
Except if you can find some creative way to that anyway. Might be possible, I don’t know.
Yeah, it might have helped to clarify that the infinitesimal factors I had in mind are not infinitely small as numbers from the standpoint of addition. Since the factor that makes no change to the product is 1 rather than 0, “infinitely small” factors must be infinitesimally greater than 1, not 0. In particular, I was talking about a Type II product integral with the formula pi(1 + f(x).dx). If f(x) = 1, then we get e^sigma(1.dx) = e^constant = constant, right?
Right. There around 1 you often can actually multiply an infinite number of factors and get some finite result.