Is every natural number positive?

3 Answers
Jan 19, 2017

Answer:

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.

Jan 19, 2017

Answer:

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.

Jan 19, 2017

Answer:

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#.