Question

Is every natural number positive?

Answer 1

Yes.

Explanation:

Natural numbers, also called counting numbers, are numbers you would normally count with. A good rule of thumb is that if you could count it on your fingers it's a natural number (double digits, triple digits are included too though). Negative numbers CANNOT be considered natural numbers.

Answer 2

It depends on if you consider 0 a natural number. If it is then every natural number is non-negative.

Explanation:

It depends on whether or not `0 in NN`. If not, then yes every natural number is positive. If 0 is a natural number then every natural number is non-negative. Some people insist that `0 !in NN`, and others say the opposite.

Answer 3

It depends...

Explanation:

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`.