Is Zero a number?

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Reply 100

KingMessi

Original post by tl,dr

Depends on who the article quotes as its source.

I was more being facetious. I didn't check. To be honest I find the whole issue very confusing.

Reply 101

Swayum

Original post by derangedyoshi

3+x=x+3, no other number has this property.

All numbers have this property.

The rest of your post may be true, but I was just pointing out that the question "is 0 a number?" isn't THAT stupid as the first 10 or so posters made it out. I gave my own opinion about whether or not it is a number later on in the thread (I said that it's difficult to define what any number means, but ultimately it's whatever we choose and we chose to define 0 as a number, so therefore it is).

Reply 102

Hipster

Within the postmodern paradigm all 'numbers' are to be deconstructed unto their non numerical 'essences'. The veneer of objective 'truth' in itself is in decay as an epistemological possibility. :pierre:

(edited 12 years ago)

Reply 103

thefifthfoo

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.

0/2 = 0 which, if you think zero is a number, is clearly a whole number (integer). It has no fractional part (unless you want to write it as 0/1, or 0 + 0/2 etc, but this can be done for any number eg 5 = 5/1 = 5/1 + 0/2 etc).

Reply 104

thefifthfoo

Original post by Tut.exe

so 0 itself causes confusion whether its a number or not and then it is a number when its 10, 100, 1000, 1000 or 0.1, 0.01 .... come on... its not even a question. The assumption that numbers have to represent physical form is absurd.

I agree with this. Take (non-real) complex numbers for example - what kind of 'physical form' does i represent? Or 3 - 7i?

Only the positive numbers represent physical form (I stopped short of saying natural numbers as you can have, for example, half a cake). I also included irrationals as, say the cake had diameter 4 and depth 1, then it would have volume 4pi cubic units, and volume is a physical form of sorts.

Negative numbers, however - what sort of form do they represent? If anything 0 has MORE form than the negative numbers, and their very definition entirely depends on 0.

Reply 105

no-fat-chicks

Original post by Ham22

IS black a colour?

I always say yes but the other day I had people shouting at me telling me that black isn't a color, it's a shade?

Reply 106

Ham22

Original post by no-fat-chicks

I always say yes but the other day I had people shouting at me telling me that black isn't a color, it's a shade?

in terms of 'light', it isn't a colour. but i always think that it is a colour when its pigment in a tube (of paint).

Reply 107

Hanvyj

After the first page I don't get why people think this is such a stupid question...

It may be commonly called a number, but its different to all the others (as people have shown) in quite fundamental ways, you can't treat it exactly the same as the other numbers etc. So why is it a stupid question?

Reply 108

Woodworth

Yea but every number is different. 0 just has more differences than most numbers.

Is infinity a number?

Reply 109

Dalek1099

Yes and is just the opposite to 0 in ways 0 is infinite.0 is a number and infinity is pretty much a number but it can't be given a full value and that demeans it.0 is a representation of how much of something there is.You haven't got a car.You've got 1 car.You've got 2 cars.It's the same.

Reply 110

thefifthfoo

Original post by Woodworth

Yea but every number is different. 0 just has more differences than most numbers.

Is infinity a number?

I tend to think that infinity is more of a concept. In any case 'infinity' is too general a concept - there is a whole set of different orders/magnitudes of infinity, starting with aleph-null (I don't have the symbol for it) which is the order of the natural numbers/integers/rationals.

Reply 111

platorepublic

Original post by TenOfThem

0 is even

Lol. That made me lol.

I intuitively thought 0 isn't a number.

But if 0 is not a number then, not all numbers are made of just numbers? Like 80, 5559404 etc. Or is the 0 in those numbers more of a digit representation rather than having anything related to 0 the non-number/number at all?

:colondollar:

Reply 112

3nTr0pY

I would argue that zero is not a number although I'm not sure what the exact definition of a number is. After all, one number divided by another number should produce another number yet 1/0 = infinity, which is not a number. I reckon if you did group theory on its ass then you'd conclude that zero is not a number.

All the people going 'duhhhh its obvious' are fools.

EDIT: Maybe 0 is the absence of number-ness? :P

(edited 12 years ago)

Reply 113

username451352

Original post by 3nTr0pY

Division is simply the multiplicative inverse. Saying a number x divides another number y simply means that there is a number z such that z*x = y. If you let x = 0, y = 4, then you get 0z = 4, which is incorrect under the Peano Axioms. Similarly as to how you can't log a negative number (to a positive base), because x^y for all positive x > 0, you can't divide by zero.

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)

Ok, so what's 0-0 equal to then? If 0 has a value, no matter how small it is, 0-0 must be smaller than that value. If it's infinitely small (which is what you're saying), you're effectively just defining the limit of 1/x as x tends to infinity - which is just zero. There's no point defining zero as that on its own though...

Defining zero as an infinitesimal is pointless in standard arithmetic.

Reply 114

qgujxj39

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?

prsom

Reply 115

aurora_dawn

I definitely think zero is a number but I think it's used more as a "barrier". It's the constant. It seperates negatives from positives. It's not odd or even. It's just ..there.

Reply 116

nuodai

Original post by kmiab

I definitely think zero is a number but I think it's used more as a "barrier". It's the constant. It seperates negatives from positives. It's not odd or even. It's just ..there.

It's even, it's 'the constant' inasmuch as any 'number' is constant, and it separates the positives and the negatives precisely because positive numbers are defined to be the numbers greater than it and the negative numbers those that are less than it; likewise 3 is the number which separates the numbers greater than 3 from the number less than 3.

To be honest, this thread's title is badly worded. The question "is zero a number?" makes no sense if the definition of 'number' is not clear and is obvious if the definition is clear. By this I mean that if the definition of 'number' is clear then it is immediate whether or not zero is a number, but if the definition is not clear then the question is asking whether a well-defined mathematical object satisfies an unspecified property.

As I said before, to me (and I'd wager most contemporary mathematicians), a 'number' is any element of the set which is the algebraic closure of the completion of the field of fractions of the smallest ring containing the natural numbers, i.e. any complex number.

To convert this to human-speak, we have the natural numbers {1, 2, 3, 4, ...} from counting -- in this setting, addition is the only real well-defined operation (since multiplication is simply repeated addition when using positive whole numbers). We want to be able to compare quantity, so we desire subtraction too -- for this purpose we obtain the integers {..., -3, -2, -1, 0, 1, 2, 3, ...} (of which 0 is a member). We also want to be able to talk about splitting things into a finite number of pieces, which naturally leads to the construction of the rational numbers (i.e. fractions of whole numbers). But this leaves 'parts of things' which cannot be subdivided into finitely many parts such that replicating the subdivisions recovers the whole of the original object, and from this discrepancy we obtain the real numbers (which allows us to include anything whose decimal expansion is necessarily infinite and non-recurring). And finally, pending the importance of being able to solve polynomial equations (which I won't go into), we want to allow negative numbers to be square-rooted -- it turns out that if we allow for this, we've done everything we need to for pretty much everything to 'make sense', thanks to the fundamental theorem of algebra.

Now, 0 is a number from the 2nd stage of this argument (i.e. that we want 'subtraction' to make sense). It would make no sense to say, for example, that 1 and -1 are both numbers but 0 isn't, because we'd expect that adding two numbers together gives a number (and 1+(-1)=0). In fact, if you accept pretty much anything other than positive integers as being a 'number', the existence of zero as a number is almost immediate; so the only context in which 0 is not a number is that in which the only numbers are the positive integers, a stance which has been obsolete for well over a millennium.

(edited 12 years ago)

Reply 117

Andythepiano

The set theory of numbers

0 is the empty set
1 is the set containing one set (the empty set)
2 is the set containing two sets (the empty set, and the set containing the empty set)
3 is the set containing three sets (the empty set, the set containing the empty set and the set that contains the empty set, and the set containing the empty set)

So yes, according to this definition at least zero is a number