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n/0 should = infinity

a number divided by zero should equal infinity. Logically, the smaller the denominator gets the larger the overall value becomes, the next logical step would be n/0=infinity, not "undefined" infinity is a defined sum or am I wrong? Maybe I just have the incorrect understanding of the word "defined".

Another conundrum: who here thinks 0.9 repeated (0.9999...) = 1?
Any number divided by and multiplied by the same constant equals itself (x * (n/n) = x)
and so 1 * 9/9 = 1,
1/9 = 0.111...
0.111... * 9 = 0.999...

0.999... = 1

I'm not sure if that's common knowledge or some abstract theory.

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Not -infinity?
anything divided by 0 is technically undefined....I think you have been watching too much of Marcus du Sautoy.....
Reply 3
Yes, you are wrong.


Another conundrum: who here thinks 0.9 repeated (0.9999...) = 1?
Any number divided by and multiplied by the same constant equals itself (x * (n/n) = x)
and so 1 * 9/9 = 1,
1/9 = 0.111...
0.111... * 9 = 0.999...

0.999... = 1

I'm not sure if that's common knowledge or some abstract theory.

It's common knowledge, though some people misunderstand and continue to disagree.
1/3 = 0.333333333....
0.333333333....*3 = 0.999999999.....
3/3 = 1

Thus, 0.999999999.... = 1
(edited 12 years ago)
Reply 5
Oh God, here we go again... I wonder what responses we get this time... :ninja:
Reply 6
See the first response: why not -infinity?
Think about the graph of 1/x. As x tends to 0 from the right, sure, it tends to +infinity. But if x tends to zero from the left, it tends to -infinity. So, by the logic you've used, at x = 0, 1/0 = +- infinity - there is no definite value.

Alternatively, you can say that if x/0 = y, x = y*0, so 0*y =/= 0, which is incorrect. Hence we simply cannot divide by zero.
(edited 12 years ago)
Any division by zero is not allowed - it is an illegal move. Any lapse in a game causes all pieces to move back to their last legal position.

We say that zero is undefined because if we didn't, we would completely **** up mathematics.

Look at this supposition, for instance:

1/0 = infinity
2/0 = infinity
3/0 = infinity

so 1=2=3. This is clearly wrong.

Or if we define 0/0 = 1 then we run into some more trouble. For example:

1/2= [1 +(0/0) + (0/0) + (0/0)+....]/[2+(0/0)+(0/0)+...] = 1

Saying that n/0=infinity is a ridiculous statement.
Reply 9
Only Chuck Norris can divide by 0.
(edited 12 years ago)
Original post by DarkSenrine
Any division by zero is not allowed - it is an illegal move. Any lapse in a game causes all pieces to move back to their last legal position.

We say that zero is undefined because if we didn't, we would completely **** up mathematics.

Look at this supposition, for instance:

1/0 = infinity
2/0 = infinity
3/0 = infinity

so 1=2=3. This is clearly wrong.

Or if we define 0/0 = 1 then we run into some more trouble. For example:

1/2= [1 +(0/0) + (0/0) + (0/0)+....]/[2+(0/0)+(0/0)+...] = 1

Saying that n/0=infinity is a ridiculous statement.


Yeah, but you don't have to do 1/0 to get that contradiction...

infinity + 1 = infinity + 2 = infinity + 3

therefore 1 = 2 = 3.

You can't treat infinity as a number, because it has no specific value.
(edited 12 years ago)
Okay, suppose n/0 is infinty. Let's say n = 1

1/0 = infinity
1 = infinity * 0

depending whether you decide anything *0 is 0 or anything times infinity is infinity, or even that it's undefined - none of these are equal to 1.

Alternatively:

1/0 = infinity
2/0 = infinity

1=2

"Another conundrum: who here thinks 0.9 repeated (0.9999...) = 1?
Any number divided by and multiplied by the same constant equals itself (x * (n/n) = x)
and so 1 * 9/9 = 1,
1/9 = 0.111...
0.111... * 9 = 0.999...

0.999... = 1

I'm not sure if that's common knowledge or some abstract theory."

Common knowledge.
0×1=00 \times 1 =0

0×2=0×1=0×20 \times 2 = 0 \Rightarrow \times 1 = 0 \times 2

Dividing By Zero...

00×1=00×21=2\frac{0}{0} \times 1 = \frac{0}{0} \times 2 \Rightarrow 1=2
The only way to understand to point \infty is via the riemann sphere.
(edited 12 years ago)
What you have to understand is mathematics which you use at a low level, eg for gcse maths and almost all applications, is not equipped to deal with infinities. It would be simply incorrect to say that n/0 is infinity because that would imply that zero multiplied by infinity = n. An infinite amount of nothing is still nothing.
Original post by boromir9111
anything divided by 0 is technically undefined....I think you have been watching too much of Marcus du Sautoy.....


Haha best line I've heard all week.
As already explained, n/0 is undefined. It just can't make sense, and leads to all sort of nonsense such as 1 = 9394ln|2|. HOWEVER, in computer graphics we do sometimes set 0/0 as 1, although my preferred approach is to use a method which wouldn't result in division by 0. (Sometimes, my love for mathematics makes my programming life so much more awkward... :P )

(Regarding 0.999... = 1 - there are a lot of proofs for it, although my favourite is to write 0.999... as an infinite sum, then finding the limit it converges to)
(Hmm, this could be the next cos^2(x) + sin^2(x) thread :tongue: )
(edited 12 years ago)
Reply 17
f(x)=1xf(x)=\frac{1}{x} where x>0x>0 , x<0x<0

limx0\displaystyle\lim_{x\to 0} f(x)=f(x)=\infty

OP, is this what you were thinking? As has already been said in post 11, you can't define it for x=0 but you can define it with limits like that instead.
(edited 12 years ago)
Reply 18
Original post by und


limx0\displaystyle\lim_{x\to 0} f(x)=f(x)=\infty

Does that make sense?


not true.

as x approaches zero then you assume x to start as a positive constant and get smaller and the value tends towards infinity, but if x approaches zero from the negative direction then it is negative infinity.

this graph shows it better
Original post by und
f(x)=1xf(x)=\frac{1}{x} where x>0x>0

limx0\displaystyle\lim_{x\to 0} f(x)=f(x)=\infty

Does that make sense?

Have you not been reading the thread? That's true but what point are you trying to demonstrate here?

The OP is talking about division by zero and you're talking about limits tending to zero from only one of the two possible directions. It doesn't answer the question. See Bakes0011 post (#11 explains it well and many other have hinted at the same thing.)

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