What's sad about this thread is that, even though the original poster is ultimately wrong, the vast majority of the people telling him he's wrong have less of a understanding of the relevant maths than the OP himself.
I can't really address every wrong thing that's been said in the thread, but here's a few I want to:
The issue is the fact that you are asking the question "What is 0/0?"
You start with 0/0 = x, and you multiply both sides by 0.
At this point you can't just jump to 0 = 0x. What you have is 0/0 * 0 = 0x.
From here you can't get to 0 = 0x without assuming a value for 0/0 to substitute in, which is the question we're asking in the first place.
Remember, when we have x/y = z, with non-zero y, and we multiply both sides by y to get x = yz, we're implying the steps x/y * y = yz, we rearrange to get x * y/y = yx. y is non-zero so y/y = 1 and from there we get x * 1 = x = yz.
But that requires we know that y/y is, and in this case, as I just said, that is the question.
Yes, 0/0 can equal any number, but which number it equals is specific on a case by case basis.
And, although it's true, it's really not very useful at all until you learn how to use it rigorously. Which is why most teachers will simply say that dividing by zero is impossible because, until it's useful, it's pretty much nothing but unnecessarily confusion.
Take the equation 5x/x and let x tend to 0, then you have 0/0 = 5.
You can, obviously, use this method to prove 0/0 can be any number you want other than infinity which, as I'm sure you know, is best done as an exception.
I can't really address every wrong thing that's been said in the thread, but here's a few I want to:
You went wrong here, and if you think about it should be reasonable clear why and it's not "You can't divide by zero." as others have said. Your original question is "What is 0/0?" if we were assuming the premise that you can't divide by zero, then your question couldn't be asked at all, so dividing by zero being impossible can't be the issue here, because we're assuming it is possible.Zack1501 said:
The issue is the fact that you are asking the question "What is 0/0?"
You start with 0/0 = x, and you multiply both sides by 0.
At this point you can't just jump to 0 = 0x. What you have is 0/0 * 0 = 0x.
From here you can't get to 0 = 0x without assuming a value for 0/0 to substitute in, which is the question we're asking in the first place.
Remember, when we have x/y = z, with non-zero y, and we multiply both sides by y to get x = yz, we're implying the steps x/y * y = yz, we rearrange to get x * y/y = yx. y is non-zero so y/y = 1 and from there we get x * 1 = x = yz.
But that requires we know that y/y is, and in this case, as I just said, that is the question.
This is incorrect. Yes, you are actually right when you conclude that 0/0 can be any number, including 0 and 5, but that's as far as it goes, that doesn't mean 0 = 5. You can't substitute the answers when ever you want. When you got 0/0 = 0, that's your answer, in this case 0/0 = 0, so you can't say that it equals 5 instead because you already know that 0/0 = 0.
Yes, 0/0 can equal any number, but which number it equals is specific on a case by case basis.
And, although it's true, it's really not very useful at all until you learn how to use it rigorously. Which is why most teachers will simply say that dividing by zero is impossible because, until it's useful, it's pretty much nothing but unnecessarily confusion.
That's not quite true.thewaever said:
Take the equation 5x/x and let x tend to 0, then you have 0/0 = 5.
You can, obviously, use this method to prove 0/0 can be any number you want other than infinity which, as I'm sure you know, is best done as an exception.
