Is zero a natural number?

[Ranjr]

Hexadecimal should instead be properly called sexadecimal.

In each the bits register as one or infinitesimal.

[The Grand Nudger]

I have jokes.....

[Carneades]

It depends.

In some contexts the set {0, 1, 2, 3, ...} is referred to as the Natural Numbers.

In other contexts Natural Numbers means the set {1, 2, 3, ...}, and the set {0, 1, 2, 3, ...} is called the Whole Numbers.

So zero is sometimes considered to be a Natural Number and other times it isn't.

[Jehanne]

I am content to say that zero is a natural number in mathematics, just not in anthropology.

[polymath257]

In set theory, the natural numbers are defined as the smallest set N such that

1. the empty set is an element of N
2. Whenever x is an element of N, so is xu{x} (the union). The set xu{x} is called the successor of x.

Then, 0 is defined to be the empty set, 1 is the successor of 0, 2 is the successor of 1, etc.

So, at the most fundamental level, it makes sense to have 0 be a natural number.

In computer science, it is common to index into a collection of data point using what is known as an 'offset'. When this is done, the
first element of the data set has an offset of 0. So, it is convenient for computer scientists to start counting at 0.

In any algebraic system, identity elements are important. So, 0 is an additive identity, meaning that x+0=x=0+x for all x. It is usually desired that number systems have such identity elements (so, 1 is an identity element for multiplication: x*1=x=1*x). So it is convenient to have 0 be a natural number when studying the algebraic properties of the set of natural numbers.

That said, most other areas of math start indexing with 1. So, we generally (but not always) see sequences and series start with an index of 1 and not 0. For this reason, most areas of math have 0 NOT a natural number.

The upshot is that it is purely a convention. Pick one or the other, let your reader know which you are using, and continue about your business.

[Jehanne]

It's kind of like the Medieval discussions of how many angels can dance on a pin! But, I suppose these types of discussions go on in the mathematics faculty lounges.

P.S. Don't trust spellcheck.

[polymath257]

It's kind of like the Medieval discussions of how many angels can dance on a pin!  But, I suppose these types of discussions go on in the mathematics faculty lounges.

P.S.  Don't trust spellcheck.

More likely in a philosophy lounge. Mathematicians are more interested in things that can be proven.

[Jehanne]

It's kind of like the Medieval discussions of how many angels can dance on a pin!  But, I suppose these types of discussions go on in the mathematics faculty lounges.

P.S.  Don't trust spellcheck.

More likely in a philosophy lounge. Mathematicians are more interested in things that can be proven.

Pssst...don't tell them. It's our secret.

[h311inac311]

In my mind Zero is not a number which can be represented in a physical way, however I do think that you can make an appeal to nature, we can say that zero is what rocks think about.
Or, as another has pointed out, that there are zero trees in my backyard.

Nothingness is a difficult concept for people to understand because our minds are always doing something and we are always surrounded by air, so technically we need something to sustain us at all times and, for the most part, even the act of thinking about nothing is still something.

[Jehanne]

In my mind Zero is not a number which can be represented in a physical way

Alternating current? In North America, there is zero current 120 times every second.