Comments on: Is 0 a Natural Number?

By: Rina Sengupta

Rina Sengupta — Sun, 02 Oct 2011 04:30:56 +0000

May be I was not able to put forward my idea clearly. I wanted to emphasize that as ‘counting’, to keep an account of any possession,came into ‘existence’ so did the natural numbers. Relation with the body parts was like ‘one -to one’ correspondence between elements of any two non empty sets. Ignorant may not distinguish between a calculator and a pineapple but not the quantity of the articles brought. It’s very difficult to answer ‘what is 2?’ or any such number to a child.We have to bring in pairs of many articles to show them the relationship existing between them.Here, we try to develop the ‘natural’ ability of the child to understand the ‘essence’ of any number.
Once that is achieved, one can gradually understand the other sections of the number system.

By: Euler

Euler — Sun, 18 Sep 2011 07:57:58 +0000

I realise that this discussion goes in circles, because despite intuition the bottom line is how the phrase “natural number” is being used and understood.

However, I personally think you are at the heart of the matter, Rina. To extend your idea. If I ask someone to show me one calculator or two books then I would be somewhat surprised if they showed me one pineapple and two space shuttles.

Yet if I asked someone to show me zero calculators or zero books then I would not be surprised if they showed me zero pineapples or zero space shuttles instead. I simply would not be able to make a distinction. Surely we cannot say that is natural! (c;

By: Rina Sengupta

Rina Sengupta — Sun, 18 Sep 2011 03:23:27 +0000

Natural numbers came naturally to mankind.To keep an account of their possessions they(I mean our ancestors) not only used their fingers & toes but also the parts of their arms and so on.0 came much later, while trying to solve certain equations, we know of. So 0 can not be a natural number.

By: Taylor

Taylor — Tue, 12 Jul 2011 23:21:32 +0000

I did not read the 90 other comments but here is my theory. Think of what it means to be a “natural” number. Why “natural” of all words? To answer this let’s first look at raw data, or numbers. These numbers have inverses, negatives, like everything else. For example, tangent and cotangent. In the natural world data is composed of objects rather than raw data. The objects essentially are complexaties of raw data.

Even “natural” language has much object like data. For example, if one was giving directions they could say travel 5 miles NE. That in essence is a vector. Both parts of the vector are necessary and since the vector is composed of more than one type of raw data type (namely direction and magnitude), the vector is an object.

The vector always has to have a positive value or else it would not exist or would be pointing in another direction contradicting its definition. However, a vector can have a value of zero. Other objects can also have instance values of zero but not negative values in nature. For example, a certain flower can have 5 petals but it could also have zero. However, this flower could not have a negative amount as mentioned earlier. Therefore, since the instance value 0 can exist in natural objects, a single natural number or an instance (raw data) of the natural object can be 0 or any other positive integer.

This is my theory. This may help clarify why computer scientists and set theorists believe that 0 is in fact a natural number. If you are asked on a test about it… just copy this paragraph. Hope this helps!

By: Pradip Baksi

Pradip Baksi — Thu, 07 Jul 2011 05:18:12 +0000

Dear Philip,
Thanks for your comment dated 22 May 2011. Please note that, as already indicated in my intervention, the said comment was not from me but, from Vladimir Andreivich Uspensky.I have merely translated and included his text in the Special Supplement to my translation of Karl Marx’s Mathematical Manuscripts [CONTENTS:
].
regards.
Pradip.

By: mike toye

mike toye — Thu, 30 Jun 2011 19:27:15 +0000

In the beginning, GOD…..
Before God created anything there was no thing! We have passed the era of NOTHING. There are things to talk, discuss and ponder over rather than no thing! Zero is not natural FULL STOP.

By: Fernando Montenegro

Fernando Montenegro — Sun, 26 Jun 2011 04:56:20 +0000

WHY such resistance to acknowledge, accept, adopt the notion that the definition of “natural number” is NOT a transcendental truth but a human convention? The connotations of the word “natural” as used in everyday language seem to contaminate its comprehension when used in specialized terminology and discourse.
Fulano says: When I say “natural numbers”, I mean the positive integers, and I don’t include zero, which is not positive.
Beltrano says: When I say “natural numbers”, I mean the non-negative integers, and I do include zero. which is not negative.
Sicrano replies to both: No problem, as long as we undertand each other in this discussion. After all [see my post no. 64 above], even Peano proposed at first that the natural numbers were {1, 2, 3, …} before revising his axioms to define them as {0, 1, 2, …}.
(Poor Murray, entrapped in this fascinating yet frustrating thread that rambles on and on and refuses to die!)

By: Bonzomi

Bonzomi — Wed, 22 Jun 2011 14:30:37 +0000

I feel …
“Murray says:
14 Mar 2009 at 10:34 am

For example, why is 5 the 5th counting number? Why name it “5? at all? Why couldn’t it be “green” or perhaps “loud” (which is the way Daniel Tammet sees it)?

So you’re right – definitions in math can be nominal.”
….like I need to answer that question even my vocabulary fails me. *struggles to find definiton of ‘nominal’*

Back to the question, I’d say that before ’5′ was invented, the person/community/walrus/anything that was responsible in inventing the number ’5′ had to choose something. It could be anything, ‘@’,’7′,’^',’÷’,'?’,'*more random symbols*’. Just anything, anything at all. That person chose one of those possible things in the set of ‘anything’ (I hope I’m explaining this right lol @-@) and he/she/it got the symbol/number/drawing of ’5′. Factors that influenced him/her/it may also be responsible to the decision of the existence of the number ’5′, but those factors can still be understood given that you can travel through time and search who made it or something. I’d say only God knows how it was done… for now… maybe… Possibilites’R'endlessz

Right now if you actually want to go through all the pain creating a time machine just to find the reason of the form of ’5′, I’d say go for it and good luck doing that. Though you might end up with a problem-loop (e.g. To solve problem x, you need to solve problem y first. To solve problem y, you need problem x solved first.) I want to borrow your time machine if you ever succeed too.

By: Dan Bach

Dan Bach — Mon, 20 Jun 2011 18:16:15 +0000

Benazir – Please allow me to read your mind ;-} I think you meant if 0 is not used as a ‘digit’ then you can’t make 10, 20, etc. But in the definition of natural numbers we just need to decide whether to include the quantity ‘zero’ in the set of natural values. Obviously there’s some controversy about that. I didn’t realize it might just be a West vs East kinda thing.

By: Murray

Murray — Sat, 18 Jun 2011 04:10:19 +0000

Ah – interesting question, Benazir. “0″ is just a representation of the number, just as 10, 20, 30 are. In some languages, there is no zero as such. In Chinese and Japanese, “ten” is written “+” and the number 20 is written (in effect) as 2×10.

So your question would not even arise in those languages!

The symbol for a number and the concept of that number are separate things, so even if “0″ is not regarded as a natural number, it doesn’t preclude 10 or 20 from being natural numbers.

Hope that makes sense.