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MATT PARKER: 0 is a perfectly good number.
And you ignore it at your peril.
The problem is it's a dangerous number.
And a lot of things can go horribly wrong with 0.
And because it is a slightly more unusual, nuanced number,
you have to be a little bit more careful with
how you handle it.
And so there are some things that you can't do with it.
So you can't divide something by 0.
And you can't have things like 0 to the power of 0.
And I get asked about these all the time.
People are constantly, why can't I divide by 0?
I want to divide by 0?
Isn't it just infinity?
Blah, blah, blah.
And so I thought I would do two things.
First of all, I'm going to show you why, no, you cannot
divide by 0.
It's not just infinity.
It's a bit more complicated than that.
And then, I'm also going to look at why you can't have 0
to the power of 0.
JAMES GRIME: OK, so this is something that we've been
asked a lot at Numberphile.
Well, you may know that something like multiplication
is just glorified adding, really.
You want to do 5 times 10?
You just add on 5 plus 5 plus 5 plus 5 10 times.
Division is just glorified subtraction.
So if I want to take a number like, oh, 20, and then divide
it by 4, I just keep subtracting 4.
So you take away 4, take away 4, take away 4.
You do that five times.
And that number, 5, that's your answer.
20 divided by 4 is equal to 5.
So it's just glorified subtraction.
That's really what it is.
Now, if I divide by 0, then that means I'm subtracting 0
over and over.
So 20 divided by 0 means I take away 0.
I've got 20.
And then, I take away 0 again.
I've still got 20.
I take away 0, and 0, and that would go one forever.
You would never get very far doing something like that,
keep taking away 0.
So 20 divided by 0?
That's infinity, isn't it?
Surely--
surely it's infinity.
And that's what I expect people to think.
Surely only a nerd would tell you differently.
That's when you cut to Matt telling them differently.
MATT PARKER: Because first of all, everyone goes, why can't
you just say that's something divided by 0?
So let's say I'm going to do a function.
I'm going to have the function of 1/x.
JAMES GRIME: We don't say something is equal to
infinity, OK?
So infinity is not a number, and it can't be
treated like number.
It's an idea.
So we can't say 1 divided by 0 equals infinity.
We can no more say that than we can say 1 divided by 0 is
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