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Well, whole numbers come up in mathematics in different ways. Of course if you're talking about cardinality you should include zero: it simply is the cardinalit
by omaranto 15y ago
Well, whole numbers come up in mathematics in different ways. Of course if you're talking about cardinality you should include zero: it simply is the cardinality of some set, you can't avoid that.
I was talking about a completely different use of numbers: numbering, that is assigning numbers as labels to things. There I think mathematicians on the whole prefer to number starting at 1 (or not to number at all and work with abstract indexing sets). Sometimes it is convenient to number starting at zero if it simplifies some formulas, but usually it doesn't matter.
- mturmon 15y agoTo continue with your example, take cases where a (finite) collection of discrete objects is summed over (unioned over, whatever). You'd let N be the number of such objects, and then twenty following pages of text would contain summations from 1 to N. This is more compact than summations from 0 to N-1. And in a certain sense, there's one less "token" to remember (i.e., if you start at 1, you have 1 and N to remember, but when you start at 0, you have N, 0, and N-1 to remember). The one that's more compact tends to be discipline-specific.