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

[ChaosGenesis]

Yes it's a number. Numbers are used to represent values. 1 represents a single something, 0 represents none of something.

I think the main issue with this whole debate is that most people are assuming that the number zero and the concept of nothing are one and the same. Perhaps the two need to be kept separate.

 

[Nannernade]

Of course zero is a number without zero we wouldn't have binary code thus technology as we know it would cease to exist.

For those that don't know binary... it's that 101010110111000 stuff.

 

[tautologico]

If you want to define that zero is not a number, go ahead. I don't know if this will be very useful, though.

Every number is an abstract concept. Is i (the imaginary unit of complex numbers) a number? Is -5 a number? All these things are abstract concepts that are considered numbers in mathematics for "pragmatic" reasons. Things like i are considered a number, and then the consequences that come from this assumption are worked out, and are actually very useful (the whole of complex analysis, which has a lot of applications today).

But if you want to say 0 is not a number, knock yourself out. What consequences come of it?

(Although it's not my main line of work nowadays, so I wouldn't consider myself a mathematician, I do have a degree in mathematics, so to establish my authority here and end this useless thread )

 

[Denamic]

Occam's razor.
Cut the bullshit.
It's used as a number, so it is a number.
Done!

 

[Andalusa]

Yes, to use your example. Yes there may be hundreds/thousands of aeroplanes in the world, there are 0 on my driveway.

 

[nuba km]

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?

you have not travelled both 6 and 0 miles you have travelled 6 miles and are 0 miles away from your origin point.
distance from origin /= distance travelled
therefore 0 /= 6

I see what your getting at but your example bugged me like hell because it was incorrect mathematically and you are trying to make (partially) a mathematical point.

edit: I should say that distance from origin is not the same as distance travelled because distance from origin can = distance travelled

 

[Doug]

Zero is digital god.

You know, though I'm not an anime fan, that made me lol.

Anywho, as for the OP, 0 is a member of the natural number set, therefore I conclude it is a member of the universal number set.

 

[DaJoW]

Of course, I understand the other side of the argument. If you don't have any apples around, then there must be 0 apples right? This starts bringing in semantics. Yes, I have 0 apples in my room at this current time. No, that does NOT make 0 a number. I can also say no apples are in my room. Is 'no' a number? Absolutely not.

I have 1 apple. I have an apple. "An" is not a number, but 1 is. It's not a sound argument. 0 can be divided, added, subtracted and multiplied in the commonly used mathematical system. I'd say that makes it a number.

 

[Doug]

Of course, I understand the other side of the argument. If you don't have any apples around, then there must be 0 apples right? This starts bringing in semantics. Yes, I have 0 apples in my room at this current time. No, that does NOT make 0 a number. I can also say no apples are in my room. Is 'no' a number? Absolutely not.

I have 1 apple. I have an apple. "An" is not a number, but 1 is. It's not a sound argument. 0 can be divided, added, subtracted and multiplied in the commonly used mathematical system. I'd say that makes it a number.

And divided by as well...

 

[Senaro]

Written mathematics existed for thousands of years without a concept or written form of zero.

 

[Senaro]

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?

you have not travelled both 6 and 0 miles you have travelled 6 miles and are 0 miles away from your origin point.
distance from origin /= distance travelled
therefore 0 /= 6

I see what your getting at but your example bugged me like hell because it was incorrect mathematically and you are trying to make (partially) a mathematical point.

edit: I should say that distance from origin is not the same as distance travelled because distance from origin can = distance travelled

The other problem is that, despite zero not being equal to six, zero and six are not answers to the same question. The question asked for two very different types of distances, one in actual space traveled over time, and one in how far away you are from your initial starting point when you stopped moving. The two answers have nothing to do with each other.

 

[PxDn Ninja]

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?

Interesting theory, but as a software engineer I have to both disagree, and provide counterpoints

Your entire presentation is based off a specific point of view, as well as a frame of reference for the data. Using programming (and thus, basic math), you can say the following:

(1-1) == 0;

So, if we subtract 1 from 1, we are left with 0. Now, if zero was not a number, that would not be possible, as you can't jump from numbers to any other form of data storage without some conversion happening.

With your travel example I have quoted, yes the distance traveled is 6 miles, but right before that you ask:

Where did you end up (relative to starting point)? 0 miles away

This is a different question involving the data than your following question:

What was the total distance traveled? 6 miles away

These are two very different questions using the same scenario. Consider that you are 6 miles from work and plan on driving it (to be consistant with your above example). We have three pieces of data.

Location A: Starting point.
Location B: Ending point.
Distance to travel: 6 Miles (OR A - B)

When you start, you are 6 miles from your destination, 0 Miles from the starting point. Half way there, you are 3 from each, (making your median point 0 as an aside), and when you arrive, you are 0 miles from your destination, but 6 miles from the start. All pieces of data are accurate, but provide a different view of the situation.

 

[Hydro Imp]

Zero can be used as a numerical value but it is not a number, it is the absence of a number. This is how I feel on the subject anyways

 

[Geekosaurus]

Felt compelled to reply to this for some reason.
Yes i think zero is both a digit and a quantity
Take basic maths for example...

Well that's part of my point. Zero is used as a placeholder. 10 is ten, 0 is zero. 10 is not one zero now is it? 0 is simply used to write a higher number numerically such as 10, 20, 30, etc.

10 is literally One Zero
It is One 10 to-the-power 2 and Zero 10 to-the-power 2's
If you get me? One 10, and Zero 1s

Or say if i walked 1 meter forwards, and then one meter back (perfectly accurately)
I would have moved 2 meters, but i would be displaced by none.. zero

I'm being mis-quoted! :/

 

[Firia]

I see numbers as a reprisentation of presence.
there are two apples on my table.
there are no apples on my table.

A number signifies the presence or the absence of something. So in that reguard, yes, Zero is a number. It's just the absence of substance.

 

[oooooooooooooooooooooooooo]

The fact that you can't divide by zero, amoungst other things, shows that zero has attributes that other numbers don't. This doesn't mean that zero is not a number, but it does mean it is at least different from other numbers (obviously I suppose).

I can see both sides of the argument, zero apples means there is nothing. Apples are not at all part of the situation if they are not there, and that could be the same with numbers. But at the same time, and number is a theoretical figure, not an object. Therefore, there is no reason to assume the same rules would apply numbers as apply to apples.

 

[Marowit]

Well, lets take a look at the number line: -2, -1, 0, oh wait....

haha, that's exactly what I was going to write.

Zero is a number. It represents something just as the number 3 does. What about exponents? n^0=1

ou can see 1 cat.
You litterally cannot see 0 cats.

One is a number, because you can give it value. 1+1=2 so it has a definative value.
0+0=0. It has no value. Zero cannot be shown outside the realm of concept, so its only an idea.

And scientifically, idea's dont exist eather. Little zappy lightening bolts in your head do.

What, Ideas don't exist in science? Not sure what you're trying to get at there, but they do in fact exist - they're called Theories...Little zappy lightening bolts (and electrochemical signaling as it's actually called) of logic churning away in my head.

And as for zero not being able to shown outside the realm of concept: if I were to show you my hand with 5 nickels, 2 dimes, and 4 quarters and ask how many pennies I have how would you answer? Zero, obviously, seems to be little concept there, and pretty much all reality. You can see the absences of cats, pennies, pick your example, and that's exactly what the number zero represents - just as one cat is represented by the number one...

 

[crudus]

Hmm, it seems like you found a book on mathematical concepts and skimmed it. This is a valid debate, but your points seem skewed. You seem to mix several concepts that should never be mixed to make your point.

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.

A vacuum isn't something you can apply a scaler[footnote]the physical number or value of what you are measuring[/footnote] to. It is like saying you have one water. The word just doesn't intrinsically come with a measurement. You can say you have a vacuum or water in a certain space but that doesn't mean you can't say you have one vacuum.

I'll just cut you off there. Sure you can say you have a vacuum, but the place you have a vacuum is defined(it's like saying "a glass of water").

Say for example you have an apple. You then eat the apple. You still have one apple, it's just in a different locale. There is always at least 1 of something (that actually exists of course), even if it is not within your present sight. There are no planes in my front driveway, but there ARE planes somewhere else.

Sorry, forgot to comment to this one. Sadly this stems from a later part of my argument. Go to the bottom and read it first. You don't have an apple. You have several parts of an apple which is not a whole apple. You probably have some sort of coarse apple sauce though.

Some people might tell me then, "Well if you can't have zero of something, then you're saying you can't have negatives either." Well, I disagree.

For another example, say you travel -1 miles forwards. Well all that means is that you traveled 1 mile BACKWARDS. Positive and negative imply direction. Zero has no direction, and no value. If a number can be described as 'A figure used to represent value', and zero has no value, then logically zero would not be a number.

Yes, vectors[footnote]scalers with direction whether you say 1 mile south or -1 miles.[/footnote] can be ne.gative, but scalers cannot. Sure you can travel -1 or 1 miles but you can't have -1 apples. Yes, 0 miles does have a direction. If you travel 1 mile north, you travel 0 miles east.

Of course, I understand the other side of the argument. If you don't have any apples around, then there must be 0 apples right? This starts bringing in semantics.

No good sir, you are bring semantics into this.

Yes, I have 0 apples in my room at this current time. No, that does NOT make 0 a number.

That is exactly what saying "have" implies. If I say "I have no apples" I mean there are none that are in my possession. It doesn't imply no apples exist anywhere which you think seems to be true. If I say "I have an apple" I am not talking about a future version of myself; I am talking about right now.

I can also say no apples are in my room. Is 'no' a number? Absolutely not.

Saying "no apples" is synonymous with(at the very least implies) "zero apples". Zero being a number.

Plus, consider the possibility that there may be, ONE SINGLE PARTICLE of an apple in my room, SOMEWHERE. Just one. It may be in the air, on my desk, on the wall, whatever. That's just .000000000000000000000000000000000001 apples or whatever, not zero.

Well, we could go into tiny fractions if we wanted, but that would be getting into semantics which you seem to dislike but bring up everywhere. Say there is part of an apple on my desk. There are zero apples on my desk but there is an apple skin or an apple core on my desk. If I just had a vial of (human)blood on my desk, would you say I had a human? I highly doubt it. Parts are not equivalent to a whole.

A number is just a pointer to a value that we have in our heads. It is hard to wrap your head around the idea of nothing or a void which I think is from where this debate stems. The real hard concept to wrap your head around is 1.

 

[Broady Brio]

Yes it is. Just remember that it also represents so much more!

 

[ThePerfectionist]

I'm willing to bet after 20 pages of this, someone has brought up the point I'm about to make, but I'm going to make it anyway.

First, I would like to reiterate the point that has already been made that saying 'no' does not imply zero can be expanded to saying 'a' does not imply one. It's ridiculous semantics and a completely invalid argument.

Moreover, I would like to talk about the idea that, to pick one of the offered examples, if you take the concept of 'This box has 1 cat in it' and remove the cat, that you have 'This box' rather than 'This box has zero cats in it'

English is a cheat language, perhaps more than any other, but I'm pretty sure this one is universal. Humans are lazy; we don't use twelve words when two will do (at least not most of the time). As a rather coarse example, when I was younger I would often say, as a statement of incredulity:

"What the hell was that?"

Fast forward a few months and it became simply

"What the hell?"

Today, I don't even bother with the first word and simply use intonation to make this a question

"The hell?"

You see? The original exclamation was five words, the shortened one is two, and they mean EXACTLY the same thing (with respect to how I use them).

Similarly, saying 'This is a box' and 'This is a box with zero cats in it' mean the same thing, but no one would say the second one because it's A) too long and B) redundant.

Also, we may not be able to observe zero somethings, but we can certainly observe the absence of something.

Consider black as a colour. It's common consensus (though I don't like it) that black is not an actual colour, but rather the absence thereof. Still, it would be foolish to say black doesn't exist. I'm wearing a black shirt. I can see the shirt. I can observe that it's black.

Likewise, I can look in a box and observe that there are zero cats.

Zero is the base counting number. I don't start with one something, I start with zero somethings and add one to it (sometimes repeatedly), which brings me to my last point.

Which of the following would you say to a box containing two cats:
"This box has two cats in it"
OR
"This box has one cat in it and another cat in it"

The first one, right? Because it's quicker, and we have devised 'two' as a faster way of saying 'one plus one'. You would certainly agree that two is a number, yes? So why should one plus one be a number and not one minus one?

For those of you that consider this too long to read, let me summarize in a sentence or two. Zero implies the nonexistence of something, and is omitted because it's faster that way and makes more linguistic sense. Further, you COULD express every number (represented as X) as X+0 but you don't because that's just X and again, no reason to write that which is redundant.

I feel I may have been a little redundant myself here, but I think it was worth it.