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Is Zero a number?

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Reply 60

hockeyjoe

Original post by Ham22

IS black a colour?

the question is, is white a colour?

Reply 61

Clez

No. if a number is a representation for an accumulation of similar items, Zero is a representation for a lack of any items at all, therefore it is not a number

Reply 62

Kennethx

Original post by SimBa14

Infinity + infinity = infinity
0 is so close to nothing it may aswell be 0 (much like a recurring number) but it's not it has a slight value. A value so miniscule you can't comphrend it but it still has a value. So 0 + 0 = 0 still remains true, yes you've added 0 but it's so crazily small in essence you've added nothing (no pun intended)

Your definition clearly violates 0+x=x. Obviously 0.0000 recurring=0. just as 1.000 recurring =1. Consider numbers as discrete infinitesimally small Points in a numberline.

(edited 12 years ago)

Reply 63

gff

Original post by W_F_HUMPHREYS

Hi,
Basically i'm doing an Extended project this year based on whether zero is a number. If anyone has any views, or simply whether they believe it is a number or not - please comment. It would be much appreciated as this will give me the view of young people from a variety of backgrounds.
Thanks.

Only if you first give me a definition of what a number is.
Do you know what a number really is, so you are asking whether or not zero is such a thing. :biggrin:

This is not a philosophy project, is it? :tongue:

Reply 64

Andythepiano

Whether you consider 0 to be a number or not, and I do, it is the most important of all the digits, since without it place value would not exist, and we would be using roman numerals

Reply 65

KingMessi

Original post by TenOfThem

0 is even

It really isn't, unless I have basic mathematical knowledge wrong. An even number is one that can be divided by two to get a whole number. This cannot be done with zero.

Reply 66

Andythepiano

I was told a story that the reason why the Romans did not put a rocket on the moon was because they had no symbol for 0.

There it was, tall and majestic, the rocket that would put the first Roman on the moon. The countdown was nearning an end

V........ IV .......... III .......... II ............ I .... (oh **** no number for zero)

so they never finished the countdown, and the rocket was never launched :biggrin:

Reply 67

Dippy Dip

I'm by no means mathematical, but I don't think that zero is a number.

Zero is nothing. It represents the absence of value. It isn't positive or negative, like other numbers are. Nothing happens when you multiply it; it isn't possible to divide with it; and it's simply ignored in subtraction and addition. What other number is like this?

Based on this, you could do a whole section on what a number is defined as, using mathematical theories or studies or whatever it is you scientists use. You can also explore it from philosophical stand points too. This extended project is unique, but it is in no way brief or stupid or a waste of time.

Reply 68

j.alexanderh

Original post by Swayum

I don't think this question is as trivial as people are making it out to be. Let's consider some properties of 0:

0 + x = x, no other number has this property

0*x = 0, no other number has this property

x/0 cannot be defined, no other number has this property

0 didn't exist in mathematics for a pretty long time until it was added by people in India, very few numbers are like this.

0 is the only finite hyperreal number as far as I know (but I could be very wrong here).

0 is both on the real number axis and the complex number axis, no other number has this property.

In base 10, 0 is clearly a very special number because it appears infinitely many times after a terminating decimal. Also, it appears infinite many times BEFORE any finite number, i.e. 456 = 000000...456. That's a lot unlike any other number. You also get this weird property that 0.9999... (recurring) = 1.0000... (recurring), i.e. it has a weird relationship with the number 9 in base 10 (or, in base k, with the number k-1)

The list goes on. Why does 0 not behave like other numbers if it is a number? Why is it so special?

How does any of this have any bearing on whether it is a number or not?

Reply 69

Pheylan

Original post by KingMessi

It really isn't, unless I have basic mathematical knowledge wrong. An even number is one that can be divided by two to get a whole number. This cannot be done with zero.

\dfrac{0}{2}=0\in\mathbb{Z}

Reply 70

SimBa14

Original post by Kennethx

Your definition clearly violates 0+x=x. Obviously 0.0000 recurring=0. just as 1.000 recurring =1. Consider numbers as discrete infinitesimally small Points in a number.

It's like iteration, a number is so cose to a value without actually being that value but can be considered to be that value as it is so close, therefore 0+x=x

Reply 71

Swayum

Original post by j.alexanderh

How does any of this have any bearing on whether it is a number or not?

Well, you need to think about the definition of what we would call a number. Suppose an alien came to Earth and asked you to explain what numbers are. How would you do it? There's no obvious way to define one I think.

Is infinity a number? Is the square root of -1 a number? Is pi a number?

Ideally, our definition of a number would be such that all numbers exhibited some similar properties. But when we look at 0, it seems to have all these special properties that other numbers don't have. It then seems strange that we'd choose to include it in this group called "numbers".

Ultimately, numbers are whatever we define them to be, and we do define 0 to be one. But there's no universal truth for why it has to be a number - we had a LOT of mathematics thousands of years before 0 was invented (I don't mean trivial maths either, I mean stuff like proving there are an infinite number of primes, Pythagoras' theorem, etc).

(edited 12 years ago)

Reply 72

Dirac Spinor

Original post by Clez

No. if a number is a representation for an accumulation of similar items, Zero is a representation for a lack of any items at all, therefore it is not a number

What about the empty set,

\emptyset

Reply 73

username570224

Original post by Mr M

Now I've heard everything. This is going to make a very brief Extended Project.

What do you think it is by the way? An elephant?

I would LOVE to see a proof for this xD

Reply 74

bordercollies10

Zero is a number, but it represents no value. I'm probably stating the obvious but take this equation:
0a+4b=4b implies that there is no a's at all, so we would probably be as well saying there is only 4 b's.
Zero is akin to nothing.
>0 implies something.
<0 can imply the inverse of an aforementioned something. .i.e. it is 6 degrees in Glasgow but it is also -8 degrees in Moscow. A virtual camera, used within 3-D modelling, may orient(by default) perpendicular to the point of origin(0,0,0). To view 5 shapes, you may place the first at(-300,0,0) then the second at (-150,0,0), the third at (0,0,0), the fourth at (150,0,0) and the fifth at (300,0,0). The virtual camera can then be orientated along the positive y and negative z axis in order to achieve the best perspective possible on the shapes.
Infinite implies an endless(or limitless) encapsulation, in other words it is everything...
In Computer Science, element zero more often than not exists. Take this one dimensional array of strings for example:
Apple...Bannana...Kiwi...Orange...Pineapple
I would therefore declare that as fruits(4)...
...say I wished to reference the contents of index 0. I would ideally equalise a temp variable to fruits(0). The temp variable would then contain the string of ASCII characters that read "Apple". On a much lower level, computers work with binary. 1 is activated, 0 is deactivated. We can see this in a byte(we're easily into gigabytes and terabytes now though!)
1 2 4 8 16 32 64 128 <<-powers of one
1 0 0 1 0 1 0 0 <<-1's are activated
1+8=9 9+32=41, hence the above byte represents 41! This could be part of a bitmap, an executable file or it could quite simply be involved in some sort of emulated register orientated operation within a RISC processor!
As soon as you add to a zero, you negate it's state of nothing...
:smile:

Reply 75

nuodai

Guys, you're being silly. Of course 0 is a number. (Except when it isn't.) At least, I'd consider a 'number' to be anything which is in the algebraic closure of the field of fractions of the smallest ring containing the positive whole numbers with respect to the natural operations of addition and multiplication... 0 certainly satisfies this.

(edited 12 years ago)

Reply 76

henryt

0 is a number, just because that's what people/mathematicians have defined it as. It just happens to be an amazing number with some super-exciting, unique properties.

Reply 77

Obadetona

Original post by Ham22

IS black a colour?

No, it's a shade

Reply 78

abc:)

Well if it's not a number what is it? :s-smilie:

Reply 79

Glutamic Acid

ZERO IS *NOT* A NUMBER do not believe these _sheep_ :sheep:

THE CUBE IS PERFECT and watch out: Look in RUSSELL and WHITEHARD's book PRINCIPIA MATHEMATICA and you will see these guys had the right idea (but good luck THE BOOKS ARE BURNED you shall won't find them in your local library HAHA FASCISTS!) Look at the people saying "YES" they know nothing of GALOIS THEORY