In terms of your remark that in counting we start at 1. I'd argue that we start at 0 and repeatedly add one for each item counted. Likewise, in multiplying we

In terms of your remark that in counting we start at 1. I'd argue that we start at 0 and repeatedly add one for each item counted. Likewise, in multiplying we start at 1, particularly in this sense: For n>0, n^0 = 1. Multiply 1 by something zero times leaves 1.