is zero a number?? as far as im concerned 0 = infinate, as when u times a number by a small number like for instance 0.000000000000000000000001 u get a big number, so times it by 0 its infinate, if drawn on a graph it wud equal tan 90 an exponantial curve, if u use the triangle graphs

N

(infinate) 0

now any number x infinate equals 0, any number divided by 0 equalls infinate but infinate x 0 dosnt equal N (any number) if some one could clear tis up for me as to wether 0 is a number n clear up my little theory it wud b much appreciated, thanx

I would say yes
0 is a number because it is a specific quanitity
infinite is not a specific quanity

But I guess it depends on how you define 'number'

Zero is weird. For one thing... how can you divide nothing up? Example:
0/2 = 0.

0/2 = 0/3 = 0/4 = 0/5 = ...

Hmm..

You've got some of that stuff a little wrong. I think you mean that when you divide one number by a small number you get a big number. If you multiply one number by a small number you get a small number. (We say "multiply," not "times." "Times" is the way you read the multiplication sign "x" out loud, but it's not a verb.) Zero is most definitely not infinite. It is about as finite as you can get. Any number that can be measured is finite, and it's really easy to measure something that you've run out of. Like zero money or beer or gasoline.

So, zero is a number. We have to be able to express any number as the sum of its real component and its imaginary component. Zero = 0+0i. Can't get any more numeric than that. (i = the square root of -1. I don't know how far along you are in your math classes. i is very important in electronics.)

Zero, the symbol "0," is also a numeral. Specifically, what we call an Arabic numeral, from the set 0, 1, 2, 3, 4, etc. The Roman numerals -- I, II, III, IV, etc. -- don't have a zero.

What about 0! ?

Factorial is generally accepted as the products of all the preceeding counting numbers (1,2,3,4,...) up to and including that number. So 5! would be 1.2.3.4.5 = 120. (it is for this reason (and others) why I am one of those people who don't think zero is a counting number. However some people do, so I ask those people the follwoing question...). If 0 is a counting number how come 0! = 1.

I know the answer, lets see who else can work it out! :)

Also, does anyone here think zero is or is not a counting number and for what reason?

I know I saw it somewhere. I had to look it up at a page.
For those who wants to know why 0! = 1 look this up.

http://mathforum.org/dr.math/faq/faq.0factorial.html

By the very definition of factoral it's the amout of possible way to arrange N items.

Since N=0, we only have 1 item "none" and it can only be arrange into 1 combination.

n! = (n+1)! / (n+1)

Therefore 0! = 1! / (0+1) = 1/1 = 1

It's -1 ! where the formula breaks down, not zero.

I would say

infinity>0

because

infinity>1 and 1>0

(0 is a number, because you can sensefully compare it to/with other numbers (you cannot compare a letter eg. a to 0 a>0 /would be possible only if a represents a number (a would then be a variable)))

Originally posted by Fraggle Rocker
n! = (n+1)! / (n+1)

Therefore 0! = 1! / (0+1) = 1/1 = 1

It's -1 ! where the formula breaks down, not zero.

That's a bit of a half-hearted definition that you're using to explain why 0! = 1, since it fixes one problem, but raises other questions (since it breaks down for non - integer inputs). Things work out much more cleanly if one simply defines x! to be the Gamma function (http://mathworld.wolfram.com/GammaFunction.html), then one simply plugs in x = 0 and gets 1.

I recommend 'The Nothing That Is' (a history of the mathematical and philosophical concept of zero) by Robert Kaplan. It's completely brilliant, (and deals with 0/1 at some length).

Is 0/0 = 1?

If so, that is strange as well. We get a number out of nothing!

No, 0/0 is not equal to 1. While it is true that
0/0= 1 is equivalent to 0= 0*1 (a true statement), it is also true that 0/0= 2 is equivalent to 0= 0*2, 0/0= 100000 is equivalent to 0= 0*100000, etc. all true statements. For any number x, the
statement 0/0= x is equivalent to 0= 0*x, a true statement.

We cannot assign any specific value to 0/0. To note the distinction between this and "1/0" where 1/0= x, for x any number gives 1= 0*x, a false statement, we say that 1/0 is "undefined" while 0/0 is "undetermined".

Well I was looking at it from the other great axiom in maths which is that anything divided by itself = 1.
Using the 2 together we can say that:

2/2 = 1 as is 2 = 1*2
0/2 = 0 as is 0 = 0*2

0/0 = 1 as is 0 = 1*0

However using the 2nd axiom, 0/0 cannot be equal to 2 because it is equal to 1.

What u have done is take a wrong equation 0/0 = 2 and then changed it around so that it read a true statement. It should never have gotten to 0/0 = 2 in the first place though because of the axiom.

Just my opinion though really....!

Its okay to multiply by zero, but its not okay to divide by zero.

I myself have divided mathematical numbering into 2 part: Calculus numbering and Normal numbering (sorry if that confuses you). In Calculus, I only consider 0 as either a very small non-negative or a very small non-positive number, like 0.000000000000000000000000000000000000000000000007
While infinite is somewhat like very big number like 293million billion trillion.
in Normal Math, infinite is some number which doesn't exist on the 'number-line' (think of either x-axis or y-axis for better visualization), while 0 is the number which is located in the middle of the axis.
Argue me.

How about this proof that everything is true

a = b
a*a = b (assume)
a = b/a
Because b = a
a = a/a
a = 1

Now, about that part that says a*a = a
a^2 - a = 0
a(a - 1) = 0
a = 0, 1
Therefore, 0 = 1

hehe. That is actually a modification of a "proof" I did in calculus to entertain myself.
0 = 0
0*0 = 0
0 = 0/0
0 = 1

How is this relevant to thread? It is not... I just did see the need to make a new thread on something as stupid as that. :p

Umm, ok I am done.

John Connellan wrote:Well I was looking at it from the other great axiom in maths which is that anything divided by itself = 1.

There is no such axiom. There is a theorem that says, in any field, anything EXCEPT 0, has a multiplicative inverse.
Applied to the rational, real, or complex numbers, that says that anything EXCEPT 0, divided by itself is 1.

curioucity wrote: In Calculus, I only consider 0 as either a very small non-negative or a very small non-positive number, like 0.000000000000000000000000000000000000000000000007

That's a very strange thing to do. In Calculus, as "Normal" mathematics, 0 is neither negative nor positive and 0.000000000000000000000000000000000000000000000007 is not 0 in any mathematics.

Even in non-standard analysis, in which one works with infinitesmals, 0 is not an infinitesmal.

4DHyperCubix

Very good. I'm so pathetic at mathematics I actually found it interesting that 0 and 1 have so much in common. ;)

Canute

Originally posted by 4DHyperCubix
How about this proof that everything is true

a = b
a*a = b (assume)
a = b/a
Because b = a
a = a/a
a = 1

Now, about that part that says a*a = a
a^2 - a = 0
a(a - 1) = 0
a = 0, 1
Therefore, 0 = 1

hehe. That is actually a modification of a "proof" I did in calculus to entertain myself.
0 = 0
0*0 = 0
0 = 0/0
0 = 1

How is this relevant to thread? It is not... I just did see the need to make a new thread on something as stupid as that. :p

Umm, ok I am done.

There's a large crack in this so-called proof :)
I numbered the lines.


Now, about that part that says a*a = a
1. a^2 - a = 0
2. a(a - 1) = 0
3. a = 0, 1
4. Therefore, 0 = 1


At line 1, you subtract both sides by a. Which means what you have left is merely an expression that will evaluate to 0 at two values of a; a = 0 and a = 1.

Dunno where you get your equality at line 4 from really. What a mind job! :)

curioucity wrote: In Calculus, I only consider 0 as either a very small non-negative or a very small non-positive number, like 0.000000000000000000000000000000000000000000000007

non-negative = positive
non-positive = negative

Make it easier on yourself!!!

non-negative = positive
non-positive = negative

Not true. Non-negative describes both positive numbers and zero. Non-positive describes both negative numbers and zero.

Well, I think I need to refine it...
Actually the reason I consider 0 that way is because many calculus expressions which show 0/0 yield particular numbers (one for each expression)

Originally posted by malkiri
Not true. Non-negative describes both positive numbers and zero. Non-positive describes both negative numbers and zero.

Not in this case Malkiri!
Since he is trying to consider what zero itself is!!!

Well, by the standard definition of the terms, that's the wrong application. He should say 'nonnegative and nonzero'.

nonnegative and nonzero? You mean that 7 x 10e-30+ I wrote?
I led everyone lost, I see......

Originally posted by John Connellan
Is 0/0 = 1?

If so, that is strange as well. We get a number out of nothing!

Surprised no one picked up on this.

If you divide anything by 0 the answer is always infinity. I.E. 1/0, 5/0, 1,000,000/0 = ∞. More precisely the limit of m/n as n -> 0 and m an element of the Reals is ∞

0 divided by anything is always zero.

Anything divided by itself is always 1.

So 0/0 has an indetermined answer,

Very good Thed, thats the proper way of explaining it. Thus zero divided by zero is indetermined.

Originally posted by John Connellan
Is 0/0 = 1?

If so, that is strange as well. We get a number out of nothing!
I can see how one would come to that assumption, since with limits, one can get something that seems to say that 0/0 is 1. For example.

lim_x→0 x = 0

However, lim_x→0 x/x = lim_x→0 1 = 1.

So to the untrained observer, it would seem like one is getting that 0/0 is 1, when one actually is not getting that result.

Originally posted by thed
Anything divided by itself is always 1.

Except 0.

Another Mathematical curiosity (upon cursory inspection), is that 0⁰ is defined to be 1 in some textbooks. However, this is usually due to the fact that lim_x→0 x^x = 1.

Originally posted by Dapthar

Anything divided by itself = 1
Except 0.


No, 0/0 can equal 1 however we cannot say it is ONLY equal to 1 becasue it is indetermined (due to what Thed said).

Depends what u mean by "="!!!

Originally posted by Dapthar

Originally posted by thed
Anything divided by itself is always 1.
Except 0.

Another Mathematical curiosity (upon cursory inspection), is that 0⁰ is defined to be 1 in some textbooks. However, this is usually due to the fact that lim_x→0 x^x = 1.

I'm truly interested in why you say that. It contradicts everything I ever read or learned as an undergraduate. Granted, as Physicist, I did not do much number theory. Please elucidate on what you say, enquiring minds want to know.

x^x = exp (ln(x^x)) = exp(x ln x)

Lim (x->0) x ln x
= Lim (x->0) ln x/(1/x)
= Lim (x->0) (1/x)/(-1/x²) ....... L'Hopital's rule.
= Lim (x->0) -x
= 0

So lim (x->0) x^x = exp (lim (x->0) x ln x)
=exp(0)
=1

I rather prove it this way

..0
0 (sorry, I just don't know how to use superscript here)
=
..1-1
0 . . .= 0/0

Argue me

curioucity:

Your argument is circular. It assumes what you are trying to prove. Therefore, the argument is not valid.

How is it circular? All he did was rewrite the problem of 0^0 into a form we already understand to not have a set value, 0/0.

4DHyperCubix

He is trying to prove that 0⁰ = 0, by assuming that 0⁰ = 0. That's circular.

Or maybe he's trying to prove that 0/0 = 0 by assuming that 0⁰ = 0. That's also circular, but with one extra step.

Sorry, help me out. Where does he assume 0^0 = 0 or claim that?

?

I just wrote 0^0 as 0/0, that's all...... I wasn't trying to say 0^0=0, nope

Originally posted by curioucity
I rather prove it this way

0⁰ = (sorry, I just don't know how to use superscript here)

Just use < sup > text you want super scripted < / sup > (without the spaces). For subscripts, just replace sub for sup.
Originally posted by curioucity
0^1-1= 0/0

Sorry, you can't write 0⁰ = 0^1-1 without dividing by zero, thus 0⁰ &ne; 0^1-1.
Originally posted by James R
curioucity:
Your argument is circular. It assumes what you are trying to prove. Therefore, the argument is not valid.
His argument is not circular, but it is still flawed due to division by 0.
Originally posted by 4DHyperCubix
Sorry, help me out. Where does he assume 0^0 = 0 or claim that?
He doesn't. See the above explanation.Originally posted by curioucity

Did you mean these were the cause?
...
0^-1=1/0
thus not good
? Yes. division by zero is the error I was referring to earlier.

Sorry. I think I drew a wrong conclusion from the way he wrote it.

I don't see any real problem with writing 0⁰ = 0/0.

Both of those expressions are indeterminate.

dapthar, I wonder if that can be 'fixed'.
Did you mean these were the cause?
0^1-1
but
0¹=0
and
0^-1=1/0
thus not good
?