An undergraduate real analysis homework problem I am working on raised the following question:
Does function $f$ need to be defined for $i=0,1$ for empty sum $\sum_{i=1}^0{f(i)}$ to be equal to zero? In other words, do any definitions of the empty sum allow for an empty sum of an undefined function to be calculated?
This problem arises in the calculation of the lower Darboux sum of a function $g:\{0\}\rightarrow\mathbb{R}$.