View Full Version : The number 0
29-11-2004, 11:56 PM
Had an interesting debate today on whether, philosophically speaking, 0, and in fact all the negative numbers, are true numbers at all. I argued they were, but my good friend who works for a merchant bank no less, suggested that since numbers served a purely quantitative function (I disagreed with this and argued that numbers had a representative function, and as such nothing still had to be represented by something for it to exist at all, using as an example the existence of a vacuum as proof that nothing can still exist as something, if you catch my drift), 0 couldn't serve as a true number, as one cannot count nothing.
Of course I argued all counting was relative, so that 2 is relative to one because 2 is merely one and another one, and 3 is relative to 2 as it's just 2 and another one, so that in order for one to count 1, one had to have 0 as a basis to begin counting. Also I questioned whether the existence of something wasn't relative to the existence of nothing, and that as such since 0 is how we quantify nothing it belonged with the other numbers, as part of the "set", if you will.
So, should 0 be considered, philosophically speaking, as not a true number at all and not part of the grouping we term "numbers", but some other form of unique character, or is it, as I believe, like infinity, a true number and a parameter within which counting is possible?
I applaud your brilliant thinking and your magnificent debating skills. You truly thought-out your argument and brought forth an excellent conclusion.
The natural numbers are to be thought of as the "counting numbers." They are 1,2,3,4,5,..., i.e. the numbers you'd use to start counting a bunch of objects. You
wouldn't use 0 to start counting, because if there are zero objects, you don't count them.
I think the best way is to think of zero as a "quantity numbers." Someone could ask "how many pork chops do you have?," and then you could answer with any "counting number," or if you don't have any pork chops, you tell them "zero." The set of numbers you can use to answer this kind of question is the set of whole numbers.
I would still say that zero is definitely a number
Zero has many meanings:
1) By itself it may mean NOTHING, zero quantity.
2) In a place value setting it means that there is no amount in that
3) Behind whole numbers it increases the whole number quantity by one
place value for each zero.
4) In the number line and in graphs it means THE POINT OF ORIGIN. All
numbers measure the distance from the point of origin, the bigger the
number, the farther the distance from zero. Also, zeroing in means to
get to the source, to target, to get to the point. What point? The
point of origin from which all numbers depart!
5) In geometry zero is a point. If we invent our own number system,
zero is any point we chose to begin.
6) In a binary system, where zero and one are the only two elements,
zero is "false" where one is "true." Binary systems make up our
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30-11-2004, 06:33 AM
Numbers can have quantitative and representative (Q & R) qualities exclusive of one another. One can have five pork chops (Q & R) or quite easily just write a statistical equation where the number five represents nothing but a component of the equation itself (purely Q). A bit more abstract; I suppose you could also have a purely R number in saying that something is valued at Pi. This just representing a geometric function without the need for any quantity. (Purely R)
Then you can travel back on yourself and say you have 5xPi making it a nice Q & R all over again.
You could have zero multiples of any of the above, or even negative amounts. The expression "-5" doesn't necessarily mean that I have stolen imaginary pork chops from you. It could mean that from a start of 20 pork chops, you have gained -5 after I started thieving.
Zero is certainly a unique character; it marks the boundery between the natural and negative numbers. I think, as I muse over the last of my Bagel, that since zero can adopt any of the above Q & R qualities, then it must be a number in it's own right. I think your merchant banker friend needs to think some more.
30-11-2004, 08:44 AM
Zero's just another ridiculous character humankind decided to make to have "philosophical" debates. To make my view short, its unique, but then again, you could have an argument about 1, and it being unique because it isn't a prime nor composite.
30-11-2004, 12:01 PM
If you've never counted "zero", you've obviously never taken inventory. ;)
I agree with Barrington's assessment.
30-11-2004, 08:38 PM
So do I incidentally, I just thought it was an interesting thing to discuss :) I made the same point about 1 as Jet did too, and argued that if 0 wasn't a number based on its "uniqueness" then neither was 1.
I also made most of the arguments IBO made, I was actually surprised at my friend since he, like myself, did A-level Maths and ought to understand the principles outlined by Barrington. Ahh well, I was right, that's always good to know :).
Speaking non-mathematically for a moment though, since clearly mathematically we can conclusively prove 0 IS a number, philosophically SHOULD it be? I think it should, because in my belief it does serve a function. My friend tried arguing that since 5+0=5, 0 "did" nothing to the 5, but I argued that taking the example of being at step 5 on, for example, the board of a boardgame, staying still still had to be quantified, as taking 0 steps forward. I also argued that simply changing the mathematical function to multiplication, 5 x 0 clearly does something to the 5, however he argued that the fact that the 0 multiplication table is all 0 is itself proof that 0 should not be considered a proper number. He furthermore proposed that since division by 0 was impossible, the mathematical system "broke down" due to 0, and that as such is didn't fit within the system.
I just think it's curious to discuss the philosophical implications for a moment, but I do agree 100% with what Barrington proposed. :)
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