...then it's impossible to define the square root of a negative number. There is no number which, multiplied by itself, gives a negative number as a result. Except, of course, for "i", which is defined as "a number which, multiplied by itself, gives minus 1 as a result"

Why can't we do the same thing for 1/0? There is no reason whatsoever.

The problem is in the definition of division.

I don't think so, I think the problem has to do with the consistency of mathematics as a whole. If you define 1/0 = G and 2/0 = G, you get in trouble. But if you define 1/0 = G and 2/0 = 2G, then it all works fine. The only problem remaining is to define 0/0 (or 0*G): is it 0, G, or a real number? That's the only problem I could find.

How many zeroes do you have to add up before you get a non-zero answer. There is no answer to that question.

That's why 0*G, or 0/0, must remain undefined. Again, it's the only problem, and a minor one at that. You can still define x/0 for any value of x other than zero, including imaginary numbers!

If you keep adding zeroes your sum remains zero. Infinity is just a language construct to say that there is no answer.

It would be wrong to define 1/0 = infinity. That's what people are tempted to think, and that does raise problems. The trick is to treat 1/0 as a number in itself, just like SQRT(-1) is a number in itself. We may call "1/0" any name we like, so long as the name is completely devoid of meaning, just like "i". "Infinity" is definitely not a good candidate.

Zero cannot exist.

Does "one" exist?

So keep the concept of absolute zero as a convenient approximation to the Planck scale

You mean, I can't have zero dollars in my bank account? That doesn't sound right.

Sorry to give you a hard time Richard, I just think this subject is not well thought by most people, myself probably included.

• wrong post title; read this before - aurino__ - November 28, 2003 - 17:48 UTC
• There's Nothing Wrong with Zero, or i . - pmartin - November 29, 2003 - 05:11 UTC