Quote from: BoscoBlue on October 15, 2014, 06:17:41 PM

Quote from: awesome31312 on October 15, 2014, 06:15:26 PM

Quote from: nsimmons on October 15, 2014, 06:12:26 PM

Quote from: awesome31312 on October 15, 2014, 06:09:07 PM

Consider these mathematical laws:

1) Any real number, when divided by zero, produces modulus and quotient zero.

2) Any real number multiplied by zero is equal to zero.

Therefore, it logically follows, that zero divided by zero is equal to zero.

Premise 1 is false, it presupposes you can divide by zero, this operation is undefined.

R/0 is an indeterminate form. It is undefined. A limiting process can be applied to an indeterminate form, but remember the episilon-delta proof, the limit never actually gets to zero, only "as close as we like"

I meant 0/x = 0

Can nothing be divided?

This is a different question, yes 0 can be divided.
By the division algorithm

a = bq+r, can this equation be made true for a=0? Of course

0=bq + r
0 = 0*0 +0

or

0 = -1*1 +1

or any other combination. If the algorithm can be satisfied any combination is divisible

[source]
http://www.fmf.uni-lj.si/~lavric/Rosen%20-%20Elementary%20number%20theory%20and%20its%20applications.pdf