Poll: Is zero a number? (Read before voting)

[randomsix]

For example, is zero even?

yes, because it can be written as 0=2x where x is a rational number/integer (can't remember which). 0 is a rational number and an integer so 0=2*0.

 

[kouriichi]

you would never have givin someone 0 $100 bills. Have you ever? Will you ever? Your using an completely illogical scenario for your arguement. This scenario would never happen. If it did, i wouldent associate "0" with what you gave me. i would associate "Nothing" with that you gave me.

You're arguing about linguistic convention. We would not say, "I gave you 1 $20 bill and 0 $100 bills," because it generally goes against linguistic convention. We do not feel the need to use '0' to signify the absence of quantity; we have other more common expressions. However, it would still be a perfectly valid statement, as '1' $20 bill was given and '0' $100 bills were given. It'd just be a little weird.

Let's put this another way. Pretend for a second that the word 'no' replaced 'zero' as part of our numerical system. The symbol '0' is no longer pronounced "ze-ro", but simply "no." Suddenly, everything sounds a little more like regular English. "I gave you 'one' $20 bill and 'no' $100 bills." or "I gave you 'one' $20 bill and 'no' kittens." If I were to replace to words 'one' and 'no' with their respective numerical symbols, we'd come get original expressions again: "I gave you 1 $20 bill and 0 $100 bills."

Simply put, we could easily have a language where 'zero' has practical value. There's nothing contradictory/wrong about it. It's just that English didn't evolve that way.

Because 0 has no value, you cant stick it to something, because that something becomes nothing.

The value of 0 is nothing. Thus 0 is nothing. Which kinda means you cannot logically stick it to something. 0 people would never exist. it would just be 0.

Look at it this way. If a-b=c why are you trying to say a-b=a-b. Doggydoor - person = doggydoor. Not doggydoor - person.

Now onto the second point. Logically, it would not be wrong for me to say, "I gave you 1 $20 bill and 0 $100 dollar bills." It would not be wrong for me to say, "I gave you 1 $20 bill, 0 kittens, and 0 puppies." '0' is a mathematical sign that symbolizes the lack of quantity, while all the other real numbers are merely symbols for various other quantities. Those two sentences are logically valid. What's happening is that we're just acknowledging something did not happen.

'a-b=a-b' is a true statement. It may be a trivial statement, but it is true nonetheless. Conventionally, we say 'a-b=a', but there is nothing logically invalid with 'a-b=a-b'.

What im trying to say is, its pointless.

0=nothing correct? We agree on that.

That imply there was nothing to begin with. But there is always something to begin with. You never begin with 0, and you can never end with 0.

You start off with $100, you get mugged. What do you have left? Your life, your hand, and the wallet you had the $100 in.

You cant have nothing. "Nothing" doesnt exist in our universe. So if 0=nothing, you cant have 0. Its that simple. Nothing is the lack of something. You cant have 0. you can have nothing, but not 0.

0 is a place holder. its there so fill in where there is not a number.

But you completely ignore the fact that you now have zero $100 bills. Sure you can have all that other stuff, but in your equation, that's what's being changed, so it's trivial to look atit from that perspective as you had that to begin with.

But i dont have 0 $100 bills. I have nothing. 0 and nothing are different. If i havent had a $100 bill to begin with, i cant have nothing. But even if i did, you cant have 0 somethings. Because 0 somethings doesnt exist.

Show me 0 kittens playing on my window. you cant, because in this realm of reality, 0 cannot be. Theres always something there. A box cant have 0 objects inside. It would still have its inner lineing. And if you ignored that, there would still be air, bugs, atoms, or something we cant see.

So 0 cannot exist because that would mean that nothing exists. And nothing cant exist. Why? Because its nothing.

 

[Rayansaki]

If Zero isn't a number then Black isn't a color.

 

[MinishArcticFox]

Zero isn't a number it's a value. There aren't many differences but this is a technicality. I can't exactly remember why it's a value as I was taught this a long time ago but I believe that it's because it doesn't fit into any of the categories for numbers (integer, imaginary numbers, etc). It also doesn't follow some rules for numbers for example:
2*5=10 therefore 10/5=2
5*0=0 however 0/0 doesn't equal 5
It doesn't comply with the communicative property so it isn't a number. This is also why you can't divide by 0 because the inverse would mean that whatever number you got by dividing by zero could be multiplied by zero to get a number that isn't zero.
12/4=3 therefore 3*4=12
12/0=?? therefore ??*0=12
Sorry if this is confusing or wrong I'm not the best teacher and this may be outdated by now since I learned it several years ago.

 

[randomsix]

you would never have givin someone 0 $100 bills. Have you ever? Will you ever? Your using an completely illogical scenario for your arguement. This scenario would never happen. If it did, i wouldent associate "0" with what you gave me. i would associate "Nothing" with that you gave me.

You're arguing about linguistic convention. We would not say, "I gave you 1 $20 bill and 0 $100 bills," because it generally goes against linguistic convention. We do not feel the need to use '0' to signify the absence of quantity; we have other more common expressions. However, it would still be a perfectly valid statement, as '1' $20 bill was given and '0' $100 bills were given. It'd just be a little weird.

Let's put this another way. Pretend for a second that the word 'no' replaced 'zero' as part of our numerical system. The symbol '0' is no longer pronounced "ze-ro", but simply "no." Suddenly, everything sounds a little more like regular English. "I gave you 'one' $20 bill and 'no' $100 bills." or "I gave you 'one' $20 bill and 'no' kittens." If I were to replace to words 'one' and 'no' with their respective numerical symbols, we'd come get original expressions again: "I gave you 1 $20 bill and 0 $100 bills."

Simply put, we could easily have a language where 'zero' has practical value. There's nothing contradictory/wrong about it. It's just that English didn't evolve that way.

Because 0 has no value, you cant stick it to something, because that something becomes nothing.

The value of 0 is nothing. Thus 0 is nothing. Which kinda means you cannot logically stick it to something. 0 people would never exist. it would just be 0.

Look at it this way. If a-b=c why are you trying to say a-b=a-b. Doggydoor - person = doggydoor. Not doggydoor - person.

Now onto the second point. Logically, it would not be wrong for me to say, "I gave you 1 $20 bill and 0 $100 dollar bills." It would not be wrong for me to say, "I gave you 1 $20 bill, 0 kittens, and 0 puppies." '0' is a mathematical sign that symbolizes the lack of quantity, while all the other real numbers are merely symbols for various other quantities. Those two sentences are logically valid. What's happening is that we're just acknowledging something did not happen.

'a-b=a-b' is a true statement. It may be a trivial statement, but it is true nonetheless. Conventionally, we say 'a-b=a', but there is nothing logically invalid with 'a-b=a-b'.

What im trying to say is, its pointless.

0=nothing correct? We agree on that.

That imply there was nothing to begin with. But there is always something to begin with. You never begin with 0, and you can never end with 0.

You start off with $100, you get mugged. What do you have left? Your life, your hand, and the wallet you had the $100 in.

You cant have nothing. "Nothing" doesnt exist in our universe. So if 0=nothing, you cant have 0. Its that simple. Nothing is the lack of something. You cant have 0. you can have nothing, but not 0.

0 is a place holder. its there so fill in where there is not a number.

You can never have a concrete example of 0 because it represents a void/lack of. But 0 can be a number because numbers are abstract ideas and do not require physical implementation to prove their existence.

But by that logic, anything people want to exist can.
its an idea. its not real. You can see 1 of something. you can count 1 of something. That makes it a number.

Now do me a favor, and try counting all the 0 objects around you. You cant count 0, because it cannot exist. The point of it being a number, is that it isnt a number. Its the void where a number should be.

You miss the point. Numbers are abstract and do not need to be physically identifiable. Take any non-integer for example. You cannot point to anything as an example of said fraction. Even something as simple as 1/2 does not exist except by definition in an abstract quality because there will always be some error to either side.

You can look up a proof for why it is literally impossible for anything in the physical world to be exactly any number, unless its basic parts are quantized (see electrons). This will probably be of the form of how it is impossible to randomly choose any number (say six, for example) out of any given continuous part of the number line because no matter how much you zoom in, you can always zoom in more, and there are always an infinite number of points between the two you can see.

Based on your logic, and according to this proof, any non-integer numbers are no longer numbers.

Edit:
If this is not true, then 0 is a number.

I believe that, based on your argument of what a number is, unless you are willing to throw out all non-integers, this is /thread.

 

[Lukeje]

For example, is zero even?

yes, because it can be written as 0=2x where x is a rational number/integer (can't remember which). 0 is a rational number and an integer so 0=2*0.

x is an integer. And contrariwise zero cannot be written in the form 2x + 1 where x is an integer.

 

[Nailz]

snip

Here's a good example for everyone. I think this may be a major point too.

Say you travel 3 miles north to work (+3). After 8 hours, you travel 3 miles south back to home(-3).

Where did you end up (relative to starting point)? 0 miles away
How far away did you travel? 0 miles away
What was the total distance traveled? 6 miles away

You have traveled 6 miles, yet your position in space is 0, because you returned to your starting location. 6 != 0 yet you traveled both 6 miles and 0 miles. Can everyone understand where I'm coming from now?

"How far away did you travel? 0 miles away" no, you traveled 3 miles away, then returned. Horrible example. Your position in space isn't 0, it's origin or X. You didn't travel 6 miles and 0 miles, you traveled 6 miles. You forget duration, which makes this example a complete failure.

 

[randomsix]

For example, is zero even?

yes, because it can be written as 0=2x where x is a rational number/integer (can't remember which). 0 is a rational number and an integer so 0=2*0.

x is an integer. And contrariwise zero cannot be written in the form 2x + 1 where x is an integer.

Are you saying that then 0 is not odd? Because that would make sense. But you lost me at contrariwise.

 

[mrpenguinismyhomeboy]

Zero is a number. You are thinking about it in terms of real life, rather then in terms of math itself. Here:

In your example, you said that even if there are no planes in your driveway, there are planes somewhere. Your basic argument was that there is never nothing, and that since there is no nothing in real life, there are no zeros in real life, and thus you attribute this as zero being a concept, not a number. Well try this on for size.

Say there is one car in your driveway. Going by your example, there is never just one car. Going by your example, every number is a concept because the number of cars is always changing, as is the number of geese and everything else.

The thing is, there is a very big difference between saying there are Zero things and there are no things. In math, absolute nothing is represented by {}, or the empty set, or N/A. The difference is that zero indicates that there is zero of certain type of object, where as the empty set indicates that there is no object to have zero of. The Empty Set is literally absolutely nothing, and to some people is one of the most important things just because it denotes absolutely no object. Your error is that you assume zero cars and no cars are the same thing, when they are in fact very very different. Saying zero cars implies that there are cars, but just zero of them, where as no cars implies that cars do not exist. At least thats how it is from a math perspective. I am aware of that both mean the same thing in common language.

On the other hand, most of math is just a giant "concept" anyway, so on a technical level you might be right. But the concept of Zero isn't more special or different than the concept of One.

 

[FluxCapacitor]

Because the lack of something isnt "number of things = 0".
Its nothing. 0 is a place holder. its there for a real number to be put in. You cant accually have 0 in our universe.

Show me one example of 0 that i can hold,touch,feel,see,eat,breath or dance to.
You cannot. Because 0 does not exist. 0 is nothing. you can hold 1 breath. you can taste the air its made of, you can feel when its cold, you can hear it when its blowing and you can see it when its broken ((like with a jet going over 1000 mph.)).

0 is not tangable because it doesnt exist.

You're arguing with me that nothing is not "number of things = 0" and with the other guys that zero is nothing. Tangibility should not be your determining factor for if a number is a number, since by this definition it is impossible to acknowledge loss numerically in any way shape or form - you cannot touch the amount of gas you've used in your tank.

Hell, all numbers are applied constructs - the properties of the apple don't change at all whether it is alone or sitting next to other apples, or not there at all. Saying that there is 4 apples in a pile applies the outside class of "fourness" to the group of apples in front of you by counting the apples. The apples themselves are not each a bit "fourish", you cannot touch the "fourness", so how can you say there are 4? Only by processing the group in your mind and applying a numerical construct. You could as easily look at a bowl that usually has apples in it, see no apples, and apply the class of "zero" to the set of apples (knowing that you were looking for apples not because you saw apples, but because you were expecting/wanting apples). Zero is an applied construct just the same as 4 - they are both numbers. If you wanted to talk only in terms of tangibles, you'd have to simply say apples.

EDIT: It seems that the maths department cavalry have arrived while I was typing. Yay!

 

[Lukeje]

For example, is zero even?

yes, because it can be written as 0=2x where x is a rational number/integer (can't remember which). 0 is a rational number and an integer so 0=2*0.

x is an integer. And contrariwise zero cannot be written in the form 2x + 1 where x is an integer.

Are you saying that then 0 is not odd? Because that would make sense. But you lost me at contrariwise.

Yes, sorry. An odd number can be written in the form 2x + 1 where x is an integer.

 

[soulfire130]

I get what you're saying but we ask these things of zero, we have to ask these of other numbers. When you say you have zero apples, you mean you have no apples in your possession, in your hands, in pocket, backpack,etc. We don't count the apple we eat because its not a apple anymore, its stumach content that WAS an apple.

 

[captainwalrus]

What im trying to say is, its pointless.

0=nothing correct? We agree on that.

That imply there was nothing to begin with. But there is always something to begin with. You never begin with 0, and you can never end with 0.

You start off with $100, you get mugged. What do you have left? Your life, your hand, and the wallet you had the $100 in.

You cant have nothing. "Nothing" doesnt exist in our universe. So if 0=nothing, you cant have 0. Its that simple. Nothing is the lack of something. You cant have 0. you can have nothing, but not 0.

0 is a place holder. its there so fill in where there is not a number.

You're correct to say that we can't 'have' nothing. However, acknowledging the absence in quantity of an object (eg. 0 $100 bills) does not fall into that absurdity. You're conflating some ideas. It's absurd to possess something that has no quantity (not lingustically-speaking, but in actual, real life), but it's not absurd to point out that an object lacks quantity or that someone does not possess an object (eg. "There are '0' kittens in this house" or "I have '0' copies of StarCraft II").

Also, I think 'absence of quantity' is a better defintion of '0' that 'nothing'. But I may just be nitpicking.

 

[kouriichi]

you would never have givin someone 0 $100 bills. Have you ever? Will you ever? Your using an completely illogical scenario for your arguement. This scenario would never happen. If it did, i wouldent associate "0" with what you gave me. i would associate "Nothing" with that you gave me.

You're arguing about linguistic convention. We would not say, "I gave you 1 $20 bill and 0 $100 bills," because it generally goes against linguistic convention. We do not feel the need to use '0' to signify the absence of quantity; we have other more common expressions. However, it would still be a perfectly valid statement, as '1' $20 bill was given and '0' $100 bills were given. It'd just be a little weird.

Let's put this another way. Pretend for a second that the word 'no' replaced 'zero' as part of our numerical system. The symbol '0' is no longer pronounced "ze-ro", but simply "no." Suddenly, everything sounds a little more like regular English. "I gave you 'one' $20 bill and 'no' $100 bills." or "I gave you 'one' $20 bill and 'no' kittens." If I were to replace to words 'one' and 'no' with their respective numerical symbols, we'd come get original expressions again: "I gave you 1 $20 bill and 0 $100 bills."

Simply put, we could easily have a language where 'zero' has practical value. There's nothing contradictory/wrong about it. It's just that English didn't evolve that way.

Because 0 has no value, you cant stick it to something, because that something becomes nothing.

The value of 0 is nothing. Thus 0 is nothing. Which kinda means you cannot logically stick it to something. 0 people would never exist. it would just be 0.

Look at it this way. If a-b=c why are you trying to say a-b=a-b. Doggydoor - person = doggydoor. Not doggydoor - person.

Now onto the second point. Logically, it would not be wrong for me to say, "I gave you 1 $20 bill and 0 $100 dollar bills." It would not be wrong for me to say, "I gave you 1 $20 bill, 0 kittens, and 0 puppies." '0' is a mathematical sign that symbolizes the lack of quantity, while all the other real numbers are merely symbols for various other quantities. Those two sentences are logically valid. What's happening is that we're just acknowledging something did not happen.

'a-b=a-b' is a true statement. It may be a trivial statement, but it is true nonetheless. Conventionally, we say 'a-b=a', but there is nothing logically invalid with 'a-b=a-b'.

What im trying to say is, its pointless.

0=nothing correct? We agree on that.

That imply there was nothing to begin with. But there is always something to begin with. You never begin with 0, and you can never end with 0.

You start off with $100, you get mugged. What do you have left? Your life, your hand, and the wallet you had the $100 in.

You cant have nothing. "Nothing" doesnt exist in our universe. So if 0=nothing, you cant have 0. Its that simple. Nothing is the lack of something. You cant have 0. you can have nothing, but not 0.

0 is a place holder. its there so fill in where there is not a number.

You can never have a concrete example of 0 because it represents a void/lack of. But 0 can be a number because numbers are abstract ideas and do not require physical implementation to prove their existence.

But by that logic, anything people want to exist can.
its an idea. its not real. You can see 1 of something. you can count 1 of something. That makes it a number.

Now do me a favor, and try counting all the 0 objects around you. You cant count 0, because it cannot exist. The point of it being a number, is that it isnt a number. Its the void where a number should be.

You miss the point. Numbers are abstract and do not need to be physically identifiable. Take any non-integer for example. You cannot point to anything as an example of said fraction. Even something as simple as 1/2 does not exist except by definition in an abstract quality because there will always be some error to either side.

You can look up a proof for why it is literally impossible for anything in the physical world to be exactly any number, unless its basic parts are quantized (see electrons). This will probably be of the form of how it is impossible to randomly choose any number (say six, for example) out of any given continuous part of the number line because no matter how much you zoom in, you can always zoom in more, and there are always an infinite number of points between the two you can see.

Based on your logic, and according to this proof, any non-integer numbers are no longer numbers.

Edit:
If this is not true, then 0 is a number.

I believe that, based on your argument of what a number is, unless you are willing to throw out all non-integers, this is /thread.

No, my logic is 0 cannot be a number because its value is nothing. it cannot be shown.
You can show half of an object. you cant show 1/4 an object. you cannot show 0 of an object.

if you try to show someone 0 kittens in 1 box. your showing them x units of air in 1 box.

0 cannot exist because its value CANNOT BE SHOWN. xD
you cannot lable something 0. and if you did, youd be labling 1 of something 0. meaning you would be lieing.

Nothing cannot exist. Nothing cannot be used. 0=nothing. thereby, by logic, 0 cannot exist. it cannot be used as a number. you can use any number as a value. 0 has a value of nothing. it has no value, meaning it cannot be used as a number, because there is always a value of something.

The only reason we use it is because its smarter then leaving a space at the end of everything, and easyer then puting nothing.

Which is best?

A:"2-2=2-2"
B:"2-2=0"
C:"2-2=nothing"
D:"2-2=chicken chicken taco"

Zero is not a number, because its value is nothing. its there for ease of use.

 

[kouriichi]

What im trying to say is, its pointless.

0=nothing correct? We agree on that.

That imply there was nothing to begin with. But there is always something to begin with. You never begin with 0, and you can never end with 0.

You start off with $100, you get mugged. What do you have left? Your life, your hand, and the wallet you had the $100 in.

You cant have nothing. "Nothing" doesnt exist in our universe. So if 0=nothing, you cant have 0. Its that simple. Nothing is the lack of something. You cant have 0. you can have nothing, but not 0.

0 is a place holder. its there so fill in where there is not a number.

You're correct to say that we can't 'have' nothing. However, acknowledging the absence in quantity of an object (eg. 0 $100 bills) does not fall into that absurdity. You're conflating some ideas. It's absurd to possess something that has no quantity (not lingustically-speaking, but in actual, real life), but it's not absurd to point out that an object lacks quantity or that someone does not possess an object (eg. "There are '0' kittens in this house" or "I have '0' copies of StarCraft II").

Also, I think 'absence of quantity' is a better defintion of '0' that 'nothing'. But I may just be nitpicking.

But thats the thing. you cannot have 0 in this universe. 0 is there for ease.
It shouldent be a number because it cannot be counted/given/taken/recived.
you can never start with 0, and you can never end with 0. because 0 is nothing, and nothing doesnt exist.

 

[LeonLethality]

The only time you can have zero of something is in a vacuum (space). And even then, you technically would call it "a vacuum", implying that there is "one" vacuum.

I know I'm focusing on the wrong part of your argument but, empty space isn't empty. It has particles and anti-particles that are constantly colliding and destroying each other.

I wish I could find my book to get a more accurate quote but that's what i remember reading.

*looks at my one and only previous post in this thread (the very first reply)*

I feel I have been misquoted.

 

[Penguinness]

Just thinking quickly, in the laws of motion every action has an equal and opposite reaction, and things that aren't moving are actually in a state of equilibrium. I'd then claim that the solution of everything is then 0. So it must be a number. But I wouldn't allocate too much time to pondering about this..

 

[cookyt]

you would never have givin someone 0 $100 bills. Have you ever? Will you ever? Your using an completely illogical scenario for your arguement. This scenario would never happen. If it did, i wouldent associate "0" with what you gave me. i would associate "Nothing" with that you gave me.

You're arguing about linguistic convention. We would not say, "I gave you 1 $20 bill and 0 $100 bills," because it generally goes against linguistic convention. We do not feel the need to use '0' to signify the absence of quantity; we have other more common expressions. However, it would still be a perfectly valid statement, as '1' $20 bill was given and '0' $100 bills were given. It'd just be a little weird.

Let's put this another way. Pretend for a second that the word 'no' replaced 'zero' as part of our numerical system. The symbol '0' is no longer pronounced "ze-ro", but simply "no." Suddenly, everything sounds a little more like regular English. "I gave you 'one' $20 bill and 'no' $100 bills." or "I gave you 'one' $20 bill and 'no' kittens." If I were to replace to words 'one' and 'no' with their respective numerical symbols, we'd come get original expressions again: "I gave you 1 $20 bill and 0 $100 bills."

Simply put, we could easily have a language where 'zero' has practical value. There's nothing contradictory/wrong about it. It's just that English didn't evolve that way.

Because 0 has no value, you cant stick it to something, because that something becomes nothing.

The value of 0 is nothing. Thus 0 is nothing. Which kinda means you cannot logically stick it to something. 0 people would never exist. it would just be 0.

Look at it this way. If a-b=c why are you trying to say a-b=a-b. Doggydoor - person = doggydoor. Not doggydoor - person.

Now onto the second point. Logically, it would not be wrong for me to say, "I gave you 1 $20 bill and 0 $100 dollar bills." It would not be wrong for me to say, "I gave you 1 $20 bill, 0 kittens, and 0 puppies." '0' is a mathematical sign that symbolizes the lack of quantity, while all the other real numbers are merely symbols for various other quantities. Those two sentences are logically valid. What's happening is that we're just acknowledging something did not happen.

'a-b=a-b' is a true statement. It may be a trivial statement, but it is true nonetheless. Conventionally, we say 'a-b=a', but there is nothing logically invalid with 'a-b=a-b'.

What im trying to say is, its pointless.

0=nothing correct? We agree on that.

That imply there was nothing to begin with. But there is always something to begin with. You never begin with 0, and you can never end with 0.

You start off with $100, you get mugged. What do you have left? Your life, your hand, and the wallet you had the $100 in.

You cant have nothing. "Nothing" doesnt exist in our universe. So if 0=nothing, you cant have 0. Its that simple. Nothing is the lack of something. You cant have 0. you can have nothing, but not 0.

0 is a place holder. its there so fill in where there is not a number.

But you completely ignore the fact that you now have zero $100 bills. Sure you can have all that other stuff, but in your equation, that's what's being changed, so it's trivial to look atit from that perspective as you had that to begin with.

But i dont have 0 $100 bills. I have nothing. 0 and nothing are different. If i havent had a $100 bill to begin with, i cant have nothing. But even if i did, you cant have 0 somethings. Because 0 somethings doesnt exist.

Show me 0 kittens playing on my window. you cant, because in this realm of reality, 0 cannot be. Theres always something there. A box cant have 0 objects inside. It would still have its inner lineing. And if you ignored that, there would still be air, bugs, atoms, or something we cant see.

So 0 cannot exist because that would mean that nothing exists. And nothing cant exist. Why? Because its nothing.

Reading over your last few posts, you have repeatedly stated that zero both equals and does not equal nothing, so, for the sake of argument, lets refrain from using any word denoting a null value or the absense of something other than zero.

You can flavor your zero two ways for the most part. You have your ordinary, garden variety concrete zero wich can denote the absense of the physical unit you attach to it, but cannot be taken out of context be removing its corresponding unit. In this case zero cats does not equal zero $100 bills; they are mutually exclusive units (unless it was the cats that ran off with your wallet, but then you have bigger problems).

You can also have the abstract zero which represents nothing at all. Of course this version of the zero can only be applied in the proper context of a numerical system, and not, as you are using it, in a physical system.

Using this definition, I can easily count zero cats onmy windowsill, even if there is one windowsill because the two do not necessarily have to relate to each other.

I cannot, however, say that by there being zero cats that thevery concept of the "cat" aquires the null value of zero because, in that situation, I am mixing the two seperate definitions of the value zero, and taking the question totally out of its context.

 

[ilion]

There are only two "numbers" after all, The element or one, and Nothing or zero. From the perception of these two arises a third ... more strange, element.