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B1 متوسط الإنجليزية 13:00 Educational

Problems with Zero - Numberphile

Numberphile · 5,844,079 مشاهدات · أُضيف منذ شهرين

إحصائيات التعلم

B1

مستوى CEFR

5/10

الصعوبة

الترجمة (319 مقاطع)

00:00

MATT PARKER: 0 is a perfectly good number.

00:01

And you ignore it at your peril.

00:03

The problem is it's a dangerous number.

00:05

And a lot of things can go horribly wrong with 0.

00:07

And because it is a slightly more unusual, nuanced number,

00:11

you have to be a little bit more careful with

00:12

how you handle it.

00:13

And so there are some things that you can't do with it.

00:16

So you can't divide something by 0.

00:19

And you can't have things like 0 to the power of 0.

00:23

And I get asked about these all the time.

00:25

People are constantly, why can't I divide by 0?

00:28

I want to divide by 0?

00:29

Isn't it just infinity?

00:30

Blah, blah, blah.

00:31

And so I thought I would do two things.

00:33

First of all, I'm going to show you why, no, you cannot

00:36

divide by 0.

00:36

It's not just infinity.

00:38

It's a bit more complicated than that.

00:39

And then, I'm also going to look at why you can't have 0

00:42

to the power of 0.

00:44

JAMES GRIME: OK, so this is something that we've been

00:47

asked a lot at Numberphile.

00:49

Well, you may know that something like multiplication

00:52

is just glorified adding, really.

00:54

You want to do 5 times 10?

00:56

You just add on 5 plus 5 plus 5 plus 5 10 times.

01:01

Division is just glorified subtraction.

01:03

So if I want to take a number like, oh, 20, and then divide

01:07

it by 4, I just keep subtracting 4.

01:11

So you take away 4, take away 4, take away 4.

01:14

You do that five times.

01:16

And that number, 5, that's your answer.

01:19

20 divided by 4 is equal to 5.

01:22

So it's just glorified subtraction.

01:24

That's really what it is.

01:25

Now, if I divide by 0, then that means I'm subtracting 0

01:31

over and over.

01:32

So 20 divided by 0 means I take away 0.

01:36

I've got 20.

01:38

And then, I take away 0 again.

01:39

I've still got 20.

01:41

I take away 0, and 0, and that would go one forever.

01:43

You would never get very far doing something like that,

01:46

keep taking away 0.

01:48

So 20 divided by 0?

01:52

That's infinity, isn't it?

01:53

Surely--

01:54

surely it's infinity.

01:55

And that's what I expect people to think.

01:57

Surely only a nerd would tell you differently.

02:00

That's when you cut to Matt telling them differently.

02:02

MATT PARKER: Because first of all, everyone goes, why can't

02:04

you just say that's something divided by 0?

02:07

So let's say I'm going to do a function.

02:08

I'm going to have the function of 1/x.

02:11

JAMES GRIME: We don't say something is equal to

02:14

infinity, OK?

02:15

So infinity is not a number, and it can't be

02:17

treated like number.

02:18

It's an idea.

02:19

So we can't say 1 divided by 0 equals infinity.

02:24

We can no more say that than we can say 1 divided by 0 is

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