0/0

Originally posted by royalchicken
True. The WHOLE POINT is that ''0/0'' doesn't mean anything. The point of that post was to show that we can find functions which would give 0/0 at some point but tend to any limit we like as x approaches that point. In that sense, 0/0 is anything we like.

Originally posted by iamatiger
i.e. 0/0 is indeterminate. If I am trying to find the bearing to travel from one point to another, I can use atan(x/y), if x and y happen to both be zero this indicates not that there is no way of getting between the two points, but that I can travel at any bearing I like as I am travelling zero distance. It is important to note that infinity is a potentia ...[text shortened]... l zero metres at a bearing of 90 degrees. In this sense 0/0 means quite a bit more than asin(2).

Originally posted by fearlessleader
i dont see how f(x,y)=0/0 w/out both x and y being 0.


i have to ask knoptfel about gallus nobelus's post, i'll get back to it later.

Originally posted by TheMaster37
That's the idea. How do you define x*y/(x^2 +y^2) in the point (0, 0)?

Whatever you choose for that point (0/0), the function will not be continuous in that point.

Originally posted by TheMaster37
That's the idea. How do you define x*y/(x^2 +y^2) in the point (0, 0)?

Whatever you choose for that point (0/0), the function will not be continuous in that point.

More exact:

let (x,y) -> (0,0) as (1/n,1/n) with n -> inf.

then the function above gives (1/n * 1/n) / (1/n*1/n + 1/n*1/n) = 1/2

let (x,y) -> (0,0) as (0,y) with y->0 then the function above gives 0

let (x,y) -> (0,0) as (1/n, a/n) with n -> inf.

then the function gives a / (a*a + 1)

now as (b/n, a/n) wich gives ab / (a*a + b*b)

there are so many possible discontinuations there 🙂

Originally posted by TheMaster37
More exact:

let (x,y) -> (0,0) as (1/n,1/n) with n -> inf.

then the function above gives (1/n * 1/n) / (1/n*1/n + 1/n*1/n) = 1/2

let (x,y) -> (0,0) as (0,y) with y->0 then the function above gives 0

let (x,y) -> (0,0) as (1/n, a/n) with n -> inf.

then the function gives a / (a*a + 1)

now as (b/n, a/n) wich gives ab / (a*a + b*b)

there are so many possible discontinuations there 🙂

Originally posted by fearlessleader
i'm seeing that the implied value of 0/0 is singular for the direction from which it is approched.

Originally posted by fearlessleader
a simmiler solution was presented regarding the nature of the following set of statements:
Statment A: Statment B is faulse.
Statment B: Statment A is true.

Statment A, this argument claims, can be true or faulse, but never both.

Originally posted by TheMaster37
Sorry, but i fail to see how a statement can be true AND false at the same time in any situation.

And apologies again for not seeing how statement A can be true OR false. Assuming either one leads to a contradiction in the argument, so statement A is neither true or false.

Our argument is; no matter what you choose for 0/0 to be, it will always lead to discussions, since no single number can be chosen to that 0/0 has a sensible meaning.

Originally posted by iamatiger
The only solution that works is:

A: Undecidable
B: Undecidable

Originally posted by fearlessleader
well yes of course we can't say that either statment is really true or really faulse, just as we cant really say that 0/0=an actual number, but in trying to find a solution, we will assign diffrent validities to the statments, but A will always be either true or faulse, same for B.

this isn't too great an anaolgy for 0/0, but it is similar. we c ...[text shortened]... w why this is the case, but this is true of any number, but never more than one at a time

i would recommend that you guyrls stop eating the cheese late at night.
0/0 has to be indeterminate, because we can never truly appreciate the exact nature of either 0 or infinity. does anyone here know of any applications where solving or defining this thing would be useful?

I have to object a little here, seems as if things are going against intuition (but with logics, that's often the case)

What i'm trying to say, is that statement A is NOT either true or false, wich you (adressing fearlessleader) keep saying 🙂

If it is either true or false, it's exactly one of them. A cannot be true, A cannot be false. So it's NOT either true or false.

I wouldn't call A undecidable, i would call it a paradox.

Undecidable is the following satement;

C: The decimal expansion of Pi contains a block of 99 nines in a row.

Originally posted by TheMaster37
I have to object a little here, seems as if things are going against intuition (but with logics, that's often the case)

What i'm trying to say, is that statement A is NOT either true or false, wich you (adressing fearlessleader) keep saying 🙂

If it is either true or false, it's exactly one of them. A cannot be true, A cannot be false. So it's ...[text shortened]... the following satement;

C: The decimal expansion of Pi contains a block of 99 nines in a row.