Thread: 0 divided by 0 View Single Post

 Quote by Anti-Crackpot Please... A classic example of how mathematics can "straightjacket" common sense. An equation with infinite solutions is NOT undefined, nor is it "indeterminate" excepting to the mind that requires finite solutions to questions with infinite answers.
I don't know if you are being sarcastic, or just trolling, or if you don't understand what is being said.

Division must satisfy the requirements of being a binary operation. That is, it must have two inputs and output. That means if I take 2 and 3, and evaluate 2 divided by 3, I need the same answer to occur. I am not allowed to say its equal to 4 on Tuesdays but equal to 5 on Fridays. Math does not work like that. We don't allow 0/0 to be "anything we wish". Logic must be consistent.

Secondly, nobody in this thread claimed the equation 0x = 0 was undefined! It simply has an infinite number of solutions, so it does not have a unique solution. That's the whole point: we can't use that equation to define division if the solution is not unique.

Thirdly, as to your assertion that
$\frac{-1+1}{-1+1} = 1$
Multiply both sides by -1 to obtain
$(-1) \frac{-1+1}{-1+1} = (-1)(1)$
We use the -1 on the left to multiply the numerator
$\frac{1+-1}{-1+1} = -1$
Rearrange the numerator
$\frac{-1+1}{-1+1} = -1$
Maybe to you $-1=1$ is "common sense". It isn't to me.