Poll: Does zero exist? - intellectual debate

[nondescript]

Believe it or not, I was discussing this the other day. My opinion is yes, zero is not, as some insist, a non-number. While in math it always affects the outcome of an equation unlike standard numbers, the same could be said for imaginary numbers, pi, and fractions. The symbol "0" represents the absence of numerical counting, but it's as valid as saying "There are no bananas." If there are 0 bananas, there are no bananas to count.
On a tangent, one might consider this theologically. Many consider themselves in a religion that is monotheistic, where you have 1 god. Others are polytheistic, so they believe in 2, 3, or maybe 1000 gods. Then there is the athiest, who says there is no god. For him, there is 0 god. This doesn't mean there is no god in the world, he just hasn't acknowledged any god or gods as his own. (Which raises the question of the difference between atheism and agnosticism, but that's a different post.)
So 0 is a number, just not a number you'd associate with anything but... nothing.

 

[FizzixNerd]

Okay, since most of you haven't taken a university level abstract math course, let me try to make this easy.

The set of real numbers is part of a set of mathematical objects known as a "field." In order to be a field, it must follow a certain set of conditions, such as for any two elements of a field, x and y, the operation defined to be addition (represented by '+') commutes. This is a fancy way of saying that:

x + y = y + x, for any x, y of the field

there are similar rules for multiplication, and other rules for adding that I won't get into. Now, here is the important part. In order for a set to be a field, there must exist an element, which is known to pure math people as the 'additive identity', such that for any element of the field, a, the additive identity added to a will give you a. In symbols:

a + (additive identity) = a

since this is long to write and hard to say, we call the additive identity 'zero' and represent it with the symbol, 0.

thus, in any field,

a + 0 = a, for any element, a, of the field.

Here is the answer for those too lazy to read all that.

Zero exists in all fields (i.e., the set of all rational numbers with addition and multiplication defined in the usual way, the set of real numbers with the same addition and mulitplication, the set of complex numbers with the same addition and multiplication), it may not exist in all SETS though.

For the purpose of the poster's question, yes, zero exists.

It exists BY DEFINITION, because you are presumably talking about the real numbers. If you are talking about some set like A = {1, 4}, it does not exist. But this has nothing to do with philosophy. Also, get over yourself and you A level math grade. Your mark is irrelevant, since the only thing you proved in this thread is that you don't understand the basics of mathematics.

Matt

PS, in fields, you cannot (BY DEFINITION again) divide by the additive identity. Trying to proves you are an idiot.

 

[Adzma]

1/1 = 1
2/2 = 1
there for n/n = 1
so you would expect 0/0 = 1

If I have no cake and I divide it into no pieces, I don't end up having a whole cake...

 

[himemiya1650]

That depends what you're talking about 0 is not a member of the empty set or any set not containing 0 but it certainly is a member of some sets i.e. {0,1} contains 0.

 

[FizzixNerd]

"That depends what you're talking about 0 is not a member of the empty set or any set not containing 0 but it certainly is a member of some sets i.e. {0,1} contains 0."

Indeed, an thus zero's existence is local to the set which you are talking about. The simple answer for the OP who has presumably never even thought that other sets exist is that zero exists.

 

[Mcupobob]

They way I see it if I have 1 apple and eat it I have 0 apples. But im not that into math so mabey I'm wrong. I think zero is suppose to repersent what people have now or in there possion.

 

[Gmano]

Does cold exist? Cold being merely the absense of heat...
Does time exist? Time being the name given to the process of entropy...

Zero only exists in the way that cold exists, in that it is the absence of heat, or, in zero's case, anything.

Since is it defined by an absence, i would say that it does not exist.

You two just forfeited your right to complain about the bitter cold. From now on, if the temperature is too low for you to tolerate, you must say "It isn't hot enough", rather than "It is too cold", as by your definition, anything higher than absolute zero is hot.

If time is the process of entropy, then time will always exist, it will never have a null value.

Deal, I already have a very high tolerance for low temperatures, and I always say that it isn't very hot.

 

[gbemery]

1/1 = 1
2/2 = 1
there for n/n = 1
so you would expect 0/0 = 1

also

n x 0 = 0

0 / 1 = 0
0 / n = 0

therefore like all numbers it must ad-hear to the rule of swapping the bottom of a fraction for the answer so e.g. 1/2 = 0.5 can be rearranged to give 1/0.5 = 2

therefore 0 / n = 0 and so 0/0 = n and as n can be any number you want this means that either it doesn't exist or it has multi-shifting qualities which means

0 / 0 = n because 0 can change its value and peramiters to suit its answer.


but keep in mind divivide means to split e.g. 1 stick can be broken into 2 pieces. However by saying n / 0 you imply that nothing is being divided so instead of it being 1 where you start division 0 can be throught of as the point of initial divide before the action to divide takes place so the division never takes place and you are always left with n - which razes the question if 0 can change its properties to 1 or if it favours one state.
p.s. please post your opinions.

You can not divide by zero. You can not divide by 'n' unless you specifically say n>0, because if you don't then you are saying that 'n' could be zero which is not valid to divide by in math. Therefore n/n = 1 or undefined. If n>0 then n/n = 1. This is the reason you learn those rules in math, you can't just tweak them to satisfy your pseudo math.

Zero doesn't have to follow the rule of 1/2=0.5 = 1/0.5= 2 because you will never have a fraction with zero in the denominator...there we are with those things called rules again. As for the rest of the 'proofs' they are just the same redundant arguments, can't divide by zero and you can't divide by 'n' or other letter because said letter might be zero unless otherwise specified. Oh so my answer is you are wrong in your way of thinking on zero.

 

[Ph33nix]

so 0/0 = n and as n can be any number you want this means that either it doesn't exist or it has multi-shifting qualities which means

0 / 0 = n because 0 can change its value and peramiters to suit its answer.


but keep in mind divivide means to split e.g. 1 stick can be broken into 2 pieces. However by saying n / 0 you imply that nothing is being divided so instead of it being 1 where you start division 0 can be throught of as the point of initial divide before the action to divide takes place so the division never takes place and you are always left with n - which razes the question if 0 can change its properties to 1 or if it favours one state.

p.s. please post your opinions.

right there you broke a math rule. YOU CAN NEVER DIVIDE BY ZERO. NEVER. PERIOD ever even 0/0 is impossible and undefined.

 

[jackelbeaver]

if zero doesn't exist then neither do decimals. or variables. or pizza rolls. cause i ate em already!!!

 

[Flunk]

No, zero is the mathematical representation of nothing. It doesn't exist and if you ask anyone else with a degree in computer science and they'll likely agree. Why else would 0 == NULL?

As a unrelated side note the Japanese word for nothing also means zero, for clarity they quite often resort to saying "zero" in English for clarity purposes.

All kidding aside zero is a representation of a lack of value and because of that it by definition it does not exist. This is akin to the fact that cold does not exist because it's just lack of molecular movement (otherwise known as heat).

 

[DownOnTheUpside]

Somehow I feel this is relevant...

Holy shit! LOL

And yes. Zero does exist.

 

[scotth266]

0 is using as a quantifier: that is, there are 0 somethings, which means that there are no somethings present.

That's the whole premise of math. So you can't ever divide by 0, because you have nothing to divide: an absence of somethings. It's quite that simple.

 

[Deleric]

The VALUE of 0 does not exist. The IDEA of 0 exists. The REPRESENTATION of 0 exists.

 

[Zeromaeus]

Yes Zero exists. They're a wonderful series of games following the exploits of a red reploid of the same name...
Oh, you meant the concept of absence. Yes. It exists by the merit that it is a representation of that which doesn't exist. Its a concept.

 

[Lord Beautiful]

As an idea, yes. In reality, no.

 

[Trivun]

Spoiler: Snipped for length

Edit : as some ppl have misunderstood my point I'll try and make it clear, Zero is a valid mathematical unit of measurement used to represent NOTHING - and because it is nothing it represents space in which nothing exists, and is a mathematical short hand or saying nothing/doesn't exist.

My logic is that it doesn't exist as it is nothing and doesn't adhear to the other rules other number do:

1 + 0 = 1
1 - 0 = 1

Therefore (n = any number)

n + 0 = n
n - 0 = n



1/1 = 1
2/2 = 1
there for n/n = 1
so you would expect 0/0 = 1

also

n x 0 = 0

0 / 1 = 0
0 / n = 0

therefore like all numbers it must ad-hear to the rule of swapping the bottom of a fraction for the answer so e.g. 1/2 = 0.5 can be rearranged to give 1/0.5 = 2

therefore 0 / n = 0 and so 0/0 = n and as n can be any number you want this means that either it doesn't exist or it has multi-shifting qualities which means

0 / 0 = n because 0 can change its value and peramiters to suit its answer.


but keep in mind divivide means to split e.g. 1 stick can be broken into 2 pieces. However by saying n / 0 you imply that nothing is being divided so instead of it being 1 where you start division 0 can be throught of as the point of initial divide before the action to divide takes place so the division never takes place and you are always left with n - which razes the question if 0 can change its properties to 1 or if it favours one state.

p.s. please post your opinions.

As a Maths undergraduate student I can safely say you have very little understanding of mathematics to the level required for this. I can also say that zero does, in fact, exist.

Look up the Ten Axioms of Numerical Analysis. Basically, they are the ten ground rules tht are absolutely vital for maths. If even one of these axioms is found to be untrue, then basically the entire subject goes down the toilet. They are the essential rules, which cannot possibly be changed. And almost all of them depend on the existence of zero.

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