Description: Any finite or infinite sum in the nonnegative extended reals is convergent. This is a rather unique property of the set [ 0 , +oo ] ; a similar theorem is not true for RR* or RR or [ 0 , +oo ) . It is true for NN0 u. { +oo } , however, or more generally any additive submonoid of [ 0 , +oo ) with +oo adjoined. (Contributed by Mario Carneiro, 13-Sep-2015)