Understanding 0/0: Infinity, 0, and 1

[madmike159]

What is 0/0.
Any thing devided by 0 is infinity, 0 devided by something is 0 and anything devided by itself is 1.

 

[Crosson]

What is 0/0.
Any thing devided by 0 is infinity, 0 devided by something is 0 and anything devided by itself is 1.

No, division by zero is undefined. If you want this thread to accomplish anything then you should do it soon before a moderator closes it.

 

[madmike159]

I started thinking aabout it when I was looking at a physics equation.

m = m0/sqrt(1-v^2/c^2)
*sorry the equation options arn't working for me*

If a particle with no mass like a photon which moves at the speed of light then its mass at rest (0) is devided by 1 - c^2/c^2 = 0. I just wondered what 0/0 was, I know that this equation has no real proof.

 

[matt grime]

The equation is only valid for massive particles, and they move slower than the speed of light, so you never attempt to 'divide zero by zero'.

There are many occasions where, if on substituted values of variables in, one would end up with 0/0. This really means you just need to be careful. There may be a removable singularity (eg sin(x)/x at x=0), a singularity like 1/x or 1/x^x at 0, or an essential singularity (such as log(z) at 0), when viewed as a function from C to the extended complex plane. The nature of the singularity may tell you something useful.

 

[madmike159]

The equation is only valid for massive particles, and they move slower than the speed of light, so you never attempt to 'divide zero by zero'.

yea I know, it just made me think about it.

 

[matt grime]

I meant to write 1/x^2, not 1/x^x, which is almost surely an essential singularity.

 

[epkid08]

0/0 is truly undefined in its nature.