I just completed a long debate with Dr. Math about how the infinite series of 1/(2^n) = 1. Our debate ended by saying that the series essentially sums to .999... which is equal to 1 if we assume that 1/oo=0. In other words: .999... = 1 - 1/oo = 1
Assuming that 1/oo=0 is nothing new. We make this assumption in calculas when determining the value of limits. However, I wonder if there is a contradiction here. Here is one issue I see: 1 = oo/oo = oo * 1/oo = oo * 0 = 0
In terms of the Intergal, the width of each rectangle is of length 1/oo. If we say that 1/oo=0, then the area would always be zero.
Does anyone on this list have any insight here or know of a reference which addresses this issue ? I think Dr. Math is tired of me asking these types of questions...