Zero is Not a Number!

[Nick]

The modern 10-based numerical system is called Hindu-Arabic for a very good reason. . . the bulk of it came from India, but the Arabs were the ones who enthusiastically adopted and disseminated it.
http://www.scit.wlv.ac.uk/university/sc ... 17/han.htm

Now, where the question of "Is zero a number?" founders, is that the word 'number' is ambiguous.

If we are talking about integers (i.e. all of the whole numbers from negative infinity to positive infinity), then zero is most certainly a number.

If, however, we are talking about "natural numbers", then some people use this term to mean non-negative integers, while others use it to mean strictly positive integers.
http://mathworld.wolfram.com/NaturalNumber.html

It may be that Mr Bean either:
1. Heard an esoteric discussion about natural numbers
or
2. Heard someone who misunderstood the significance of the question "Is zero a natural number?" (The answer being, 'the term is ambiguous, so avoid it if the answer to this question actually matters')

[haas mark]

I say check out a nice abstract algebra book. Any one will do.

Mhmm.......*poke*

[haas mark]

...

[Malecoda]

Why nevermind? I'll poke you!

[haas mark]

Why nevermind? I'll poke you!

Never mind about the post.......it was something that didn't need to be there, and you can't poke me!

[Malecoda]

I can poke your avatar

[haas mark]

I can poke your avatar

Don't go there, I might like it.

[Einhander Sn0m4n]

I can poke your avatar

Don't go there, I might like it.

Same with me

[haas mark]

I can poke your avatar

Don't go there, I might like it.

Same with me

*thwap* Nobody asked you!

[Einhander Sn0m4n]

Hey I'm the one who spotted the n00b first!
*whips out a Quake 3 Rocket Launcher*
Care to Ride My Rocket?™

[haas mark]

Hey I'm the one who spotted the n00b first!
*whips out a Quake 3 Rocket Launcher*
Care to Ride My Rocket?™

Care to take your implications elsewhere? *balefires Rocket Launcher*

[Einhander Sn0m4n]

Hey I'm the one who spotted the n00b first!
*whips out a Quake 3 Rocket Launcher*
Care to Ride My Rocket?™

Care to take your implications elsewhere? *balefires Rocket Launcher*

Oh You're no phun!
*whips out another Rocket Launcher*
You'll see I have an endless supply of these... Let's just say that me and a Vadrigar had some fun in the bedroom
oh btw back on topic: ZERO IS A NUMBER!!!!

[haas mark]

Hey I'm the one who spotted the n00b first!
*whips out a Quake 3 Rocket Launcher*
Care to Ride My Rocket?™

Care to take your implications elsewhere? *balefires Rocket Launcher*

Oh You're no phun!
*whips out another Rocket Launcher*
You'll see I have an endless supply of these... Let's just say that me and a Vadrigar had some fun in the bedroom
oh btw back on topic: ZERO IS A NUMBER!!!!

It is, but don't make me balefire...well....a certain *pair* of zeros, einy...

[Einhander Sn0m4n]

Care to take your implications elsewhere? *balefires Rocket Launcher*

Oh You're no phun!
*whips out another Rocket Launcher*
You'll see I have an endless supply of these... Let's just say that me and a Vadrigar had some fun in the bedroom
oh btw back on topic: ZERO IS A NUMBER!!!!

It is, but don't make me balefire...well....a certain *pair* of zeros, einy...

Hey they're not zeroes, besides your balefire is no match for my ISD-level shields!

[Malecoda]

Proof that Zero is a Number

Look at any polynomial (in the space double-struck P sub-n, blah blah dee) and how to solve for x. Take SQX, Solve the Quadratic for x:

ax^2 +bx+c = d, for a, b, c, d in some field F. R is a good one. How do you solve that? Set d = 0, which gives

ax^2+bx+c2 = 0, where c2 absorbs the number d, that is c2 = c - d.

Well, we know that a, b, and c2 are all real numbers, because we said so and this is deductive logic. Any number plus another number gives another number. If it didn't, arithmetic would be quite different. But if you assume 0 not in R, not a number, then you have a contradiction, neh? So 0 is a number. [/b]

[Larz]

[darkstar]Zero is not a number because it is a circle and thus is infinity. Hence, it is all numbers and yet no numbers at all. It is a concept thus not a number. Much like any number that has zeros in it, any number with the number 6 or 9 in it, and as for 8 it is a double infinate/nothingness so it cancels out, thus 8 really doesn't exist. [/darkstar]

[Malecoda]

That was only the first step in SQX, sorry. After setting the right side = 0, then you apply the quadratic formula,

x = [-b + or - (b^2 - 4ac)^(1/2)]/2/a. That was what I meant by SQX. This is really SQX1, because there is an alternate, called SQX2. Call the discriminant b^2-4ac = s, just because. Take the "plus case":

x = [-b + sqrts]/2/a and multiply by one in the form of the conjugate over itself (not the complex conjugate necessarily, but see how this works out, it's cool):

1*x = [-b + sqrts]*[-b - sqrts] b^2 - sqrts^2 b^2 - s
-------------------- = ----------------- = --------
2a(-b - sqrts) -2a(b+sqrts) -2a(b+sqrts)

= b^2 - b^2 + 4ac
-------------------------- = x.
-2a(b + sqrt[b^2-4ac])

[Malecoda]

Whoa, that's like impossible to tell what I was thinking. But ah, you do end up with 4ac divided by the quantity -2a(b+sqrts) as x. For, what happens to SQX1 as a approaches 0? You still have a quadratic, only now the solution becomes more and more unstable, until small differences in input cause wild swings in output. Another proof that zero is a number, I think much more lax, would be that the limit of a fraction goes to zero as the denominator reaches infty. The fraction is always a number, isn't it? And R encompasses the irrationals, which are uncountable. What happens to SQX2 as s -> infty?

[haas mark]

*ahem* As I stated in my first post, zero is, by mathematical definition, a number.

[Malecoda]

Prove your statement.

[haas mark]

Prove your statement.

Zero is a whole number. It is an integer. Both of which are part of the group of real numbers. Therefore, zero is a number. Look it up in a pre-algebra book.

[Malecoda]

How can you be sure it's a whole number if you don't know if it's a number or not?

[haas mark]

How can you be sure it's a whole number if you don't know if it's a number or not?

Because by definition, whole numbers include all integers atarting from zero.

[Malecoda]

"Zero is a number because zero is a whole number?" I am not sure why you are taking exception to my simple proof. I answered the question and I removed all room for argument, so this is what our conversation has become? Yecch.

What is 0/0? If zero were a whole number, it would be 1. What is 0+0? Don't numbers have to add up? The other whole numbers do. Hmm. What about 0.00000000..., wouldn't that be a rational number, a ratio of whole numbers? Or would that be 1, 0, or infinity? What if you looked at zero not as "nothing" but as the singular point of a sign change on the real number line? What if you regard it as the additive identity, thus meeting one of the conditions for a group? If it were "nothing" how could you do that--how could you move it around the = to solve unknowns?

So: "is it a number or not?" Suppose it's not. Then when you take ax=b, ax-b= 0, all of a sudden, ax-b isn't a number. But a, x, and b are all numbers. I'm done lathering and repeating, time to rinse.

[data_link]

"Zero is a number because zero is a whole number?" I am not sure why you are taking exception to my simple proof. I answered the question and I removed all room for argument, so this is what our conversation has become? Yecch.

Dictionary definition. Much simpler than convoluted logic.