>>13136956>By actual definitionWhich definition. There are different definitions, you mong.
>>13136939We never consider zero to be neither. It is always even, as you pointed out.
>>13136891What do you mean? Adding unity to a set that contains unity does nothing.
>>13136857The natural numbers without zero are a semi-group. The natural numbers with a zero are a monoid. I see a lot more uses of a monoid than a semi-group. Additionally, the natural numbers without zero can already be succinctly written as while there is no such succinct way to write the natural numbers with zero unless you define it as Furthermore, when constructing the natural numbers from sets, you start at and then continue from there. This makes the subsequent construction of integers much easier, as you don't need to deal with constructing a new zero element. Therefore, it makes more sense to include zero in the natural numbers.
