Every natural number is positive?

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##.