Poll: Does zero exist? - intellectual debate

[Denmarkian]

I can go with that - thou you could always be difficult and argue 0.A* (pretend * is above value A and stands for infinite sign).

0.A* x 10 = A.A*

ergo 10 = A.A* and 1 = 0.A* and therefore you could say 9 = A so proportional expansion

Ghrk... no. No, you can't.

If you are postulating that you could multiply any real number, raised to the infinite power, by another real number, you're insane. Every number raised the the infinite power is equal to infinity. You cannot multiply infinity by any real number and get any answer other than infinity.

Not to mention that any real number less than one, raised to the infinite power, will be equal to that real number's inverse raised to the negative infinite power, which means that the limit of the number's value is zero. Again, the concept is that you can't multiply zero by any real number and get anything other than zero.

To go back to your original question; in the real world, there is no such thing as zero. When you have zero of any quantifiable object, it means you have none of the object in question. When you are moving at a rate of zero in units of distance over time, it means you are not moving.

Conversely, Mathematics depends on having a quantifiable value relating to the absence of something. You cannot have equations with addition and subtraction without zero: It would be impossible to solve X + 1 = Y - 15 if we were not able to declare that X + 14 - Y = 0. If you had two mathematical statements, and the subtraction of one from the other was not zero, then you could not say that the two statements are equivalent.

It's when you introduce the concept of zero to other arithmetical functions such as multiplication, division, exponents, and so on that the concept of zero needs to change in order to work within these other functions. While we can state with relative certainty that 0*n = 0 and 0/n = 0, just like 0 + n = n, and n - 0 = n; things need to change when we try to do more complex things with zero.

You cannot divide by zero, no matter what. Even with attempting to divide zero by itself, you cannot divide by zero. You cannot divide any real number into enough pieces so that each piece represents the absence of the object. It doesn't work that way.

0/0 and infinity/infinity are indeterminate forms of a function. It is impossible to solve because you have no way of determining the ratio in terms of a real number multiple.

Think of it this way:
Say I have zero ducks, and I want to divide my ducks into groups so that I can give my friends zero ducks each. How many people can I give zero ducks to, out of my zero ducks to begin with?

Conceptually, I can give zero ducks to an infinite number of friends because there are no ducks to divide, and I am giving no ducks to everyone. BUT I cannot tell each of my friends how much of my zero ducks I am giving them, because there is no way to quantify which part of my zero ducks is their zero ducks.

So, zero both exists and does not exist; it is both a core concept of Mathematics, and it doesn't exist in the real world.

 

[Nicolai]

To take this into graphical theory, there are proofs for the existence of zero, they just also require a proof for the existence of infinity.

I'm not sure I accept your postulate that the absence of something is its opposite, as shown by zero. There is an absence beyond zero, as others have already pointed out with negative numbers. If I have 1 apple, the opposite of that is not zero apples, that is simply an absence, but -1 apples.

Now to get complicated. Cartesian Coordinate geometry defines any two lines at 90 degrees to each other to always multiply the products of those gradients to be -1

y = x and y = -x are at right angles to each other, the gradients are 1 and -1 which give a product of -1. This always works.

Now, take the equations y = 1, which has a gradient of 0 and x = 1, which has a gradient of infinity, these products must also equal -1

Therefore,

Infinity x 0 = -1, or 0 = -1/infinity, similarly -1/0 = infinity (Yes, I divided by 0, but infinity is undefinable, so I can). So a definable zero is partially reliant on the definition of the undefinable.

However, we also can not use our computers without the existence of a zero state, which we use to signify information which is not there, to differentiate from information which is, so although we can't properly define it, we can harness its power. Incidentally, we can also do this with imaginary numbers which have a role in capacitors.

 

[beddo]

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.

Yes, zero does exist. Though it is not shorthand for saying nothing exists, that is defined as the 'empty set'

Firstly, your argument does not state the number set you are applying it too. For example some definition of the 'natural number set' do not include zero.

In the 'Reals' which is what you appear to be referring to it is true that:

n + 0 = n
n - 0 = n

These form part of the axioms or 'rules' that define the Reals.

It is also true that:

n / n = 1 except where n = 0. The nature of dividing by zero means that an entire axiom is taken up explaining it.


Interestingly you do begin to get near the answer:

"therefore 0 / n = 0 and so 0/0 = n and as n can be any number you want"

(Although your maths here is wrong as multiplying by 'n' on both sides gives: 0 = 0 x n and hence 0 = 0.)

Dividing by 0 gives "any number you want". Dividing is not a way of splitting an object but saying how many of 'a' goes into 'b'.

How many '0's are in '0'? As many as you want! That's why we say that dividing by zero is undefined. The same for any number, how many zeros in '1'? infinitely many! 1, 2, 3, 52.6!


Of course as you moves into calculations involving number that approach zero and so on we use limits and the algebra of limits, if you will, to do the calculations.

 

[Aardvark]

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.

 

[beddo]

I can go with that - thou you could always be difficult and argue 0.A* (pretend * is above value A and stands for infinite sign).

0.A* x 10 = A.A*

ergo 10 = A.A* and 1 = 0.A* and therefore you could say 9 = A so proportional expansion

Ghrk... no. No, you can't.

His quote is pointing out a contradiction in the logic and 'showing' in the vaguest sense that dividing by 0 is not a valid operation.

 

[beddo]

There are no apples in my room. I have 0 apples.

There is a 0% chance that in the next four seconds, thousands of dogs are going to rain from the sky.

Zero exists.

It's not impossible that dogs could rain from the sky.

 

[beddo]

Of couse it doesn't exist! It represents nothing. How many cows do I have 0!

If it doesn't exist how can you write it down? How can you understand that you have no cows?

 

[Arrogancy]

From a purely logical standpoint, no, zero does not exist. It is merely a title we assign to something that has no value. Zero was created solely for the purpose of aiding in mathmatics to help keep the number system organized. However I accept the zero as real since it does its job well and I cannot imagine life without it.

 

[Steveh15]

snip

At it's most basic it's to do with the difference between counting the natural numbers (1,2,3 etc) and the real numbers (every number that is not an imaginary number - if that doesn't make sense then just consider it every number).

Natural numbers are said to be countable and (this is where your belief may falter), there are the same number of even numbers as there are natural numbers. Think about that - the sequences (1,2,3...) and (2,4,6...) have the same number of elements. It might seem strange, but that is also the answer to your infinite hotel problem.

Real numbers are said to be uncountable. The basic premise is that there are more numbers between 0 and 1 than there are natural numbers. Lets say it was possible to count up to infinity, and you assigned a decimal between 0 and 1 to each natural number. The full explanation is very long winded but consider that whichever decimal you had you could always add a digit to the end to make a different one.

That sort of makes sense and explains what I always thought.
ie There are an infinite number of Real numbers between 0 and 1
" " 0 and 2
but clearly there are more real numbers between 0 and 2 than there are 0 and 1. Are there double? Do operations such as doubling and multiplication even apply to infity.

Anyway the answers i remember are
a) ask everyone to move up one room. person in room 1 goes to room 2, person in room 1 million goes to 1 million and 1 etc, leaving room 1 free for a new guest
b) Ask everyone to go to the room number double of their current number. Person in room 2 goes to room 4, room 108 goes to 216 etc. New set of inifinite people go to the odd rooms.

 

[Tucker154]

0 is nothing and non-existent because it over all has no purpose to serve but a place holder and the marker between positive and negative.The reason why i believe this:
1+0=1
1+0+0=1
1+0+0+0=1
1+0+0+0+0=1
1+0+0+0+0+0=1
No matter how many times I add zero at ends the same,1.
n+0=n no matter what
In the long run,the only part that actualy matters is (1) nothing else.

 

[OhJayEee]

We can agree that nothing does not technically exist, because it simply indicates an absence of existing things. However Zero (as in the number) can exist because it is our numeric representation of nothing. Saying zero doesn't exist is like saying the word "nothing" doesn't exist, just because it's our linguistic representation for an absence of things.

Off topic however, thanks for putting up an intellectual discussion. Nice change of pace.

 

[Denmarkian]

I can go with that - thou you could always be difficult and argue 0.A* (pretend * is above value A and stands for infinite sign).

0.A* x 10 = A.A*

ergo 10 = A.A* and 1 = 0.A* and therefore you could say 9 = A so proportional expansion

Ghrk... no. No, you can't.

His quote is pointing out a contradiction in the logic and 'showing' in the vaguest sense that dividing by 0 is not a valid operation.

But he's using the proof that 0.99999999(repeating) = 1

THAT HAS FUCK ALL TO DO WITH ZERO!

 

[Weaver]

Does 1 exist?

 

[Steveh15]

Does 1 exist?

No one likes a smart arse : P

 

[LewsTherin]

Zero is how many sharks you currently have eating you.

Exactly.

 

[KurtzGallahad]

Zero is a concept, the concept exists, technially as a null-nomber it exists but not as a number, in the same way a vacuum is an absence of matter and exists

 

[Asturiel]

If zero doesn't exist, what are you using in your equations?

I use imaginary things in equations all the time, you dont?

Please dude, it's the weekend. I don't need to think about this.

....it's monday...

ladies and gentlemen! i give proof of the existence of zero!


--> 0 <--

Ladies and gentlemen I shall pass judgement on this unfunny joke repeated *Slaps*

OT: Zero is theoretical. A number that exists to represent something that does not. If your looking for ultimate 100% never going to fail once ever in the history of ever your looking in the wrong universe my friend. Exceptions exist, everywhere even in your precious mathematics.

 

[madarame42]

zero exists in my wallet.

 

[Weaver]

Does 1 exist?

No one likes a smart arse : P

Believe it or not, I'm a mathematics major with a minor in philosophy, and these things have been extensively debated in history.

The Greeks, while having no notion of 0, had some interesting ideas on this. Especially the likes of Plato. While he was most certainly wrong, it's interesting to imagine that each cardinal number has a platonic form.

Later philosophers like Locke probably would have noted that an item which has a "Oneness" is simply a substance with the characteristic of oneness to it. However, thinking about zero I believe he would have had trouble with "nothing" having a characteristic as it is not a substance.

If we're going for an actual mathematical perspective, numbers don't actually "exist" they're an abstract toolset used by humans.