21 Jun It depends… Natural numbers are always non-negative and wh
It depends… Natural numbers are always non-negative and whole but sometimes ##0## is considered a natural number and sometimes it is not. One way of thinking of it is as follows: A cardinal number is a number that counts the number of items in a set. Since it counts items it is whole and cannot be negative but the empty set is a set containing ##0## elements. So ##0## is a cardinal number. An ordinal number tells you the order in which items occur. Ordinal names are first second third etc. corresponding to numbers ##1 2 3…##. It is natural to start from ##1## when speaking of a sequence of items. Like cardinal numbers ordinal numbers are whole and non-negative but ##0## is not an ordinal number. Natural counting numbers could refer to a cardinal or ordinal type of usage. So there are good reasons for starting from ##0## or from ##1##. It really depends on the context. Since the symbol ##NN## for the natural numbers is ambiguous it may be best to instead use ##NN_0## to stand for natural numbers starting from ##0## and ##NN_1## for natural numbers starting from ##1##.
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