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#### 如何证明2=1

Good day, welcome to the Tecmath Channel.

What we’re gonna be doing in this video is

I’m gonna prove to you that 2 is equal to 1.

Okay, so you might be thinking

there’s no way you can prove this.

But sit back. I’ll show you.

Alright, the first thing I’m gonna do is

I’m gonna use two letters to do this.

They’re gonna be a and b here.

And we’re gonna say these guys are equal to one another.

So a could be equal to 1

but b could be equal to 1.
b也等于1
Alright, so let’s start off with this.

We’re gonna say that a is equal to b.

Alright, I think we can agree on that one.

The first thing I drew this equation

is I am going to multiply it by a.

So if we were to do this,

a times a is a²
a乘以a等于a²
and a times b is ab.
a乘以b等于ab
Now to both sides what we’re going to do

is we are going to take away b².

So maybe you want to do that and see what we get.

If you get a² and take away b²,

you get your a² take away b²

and this side you’re gonna get ab take away b² .

The next thing I’m gonna do,

I’m gonna get you to do

is we are going to factorize this.

Okay, we’re going to factorize this.

Alright, maybe you even attempt doing this.

What you’ll notice is this is

the difference between two squares here.

So a² take away b² becomes the following

and becomes a take away b and a plus b.

And if you don’t believe that, expand it out.

That’s what…this becomes here.

This one here you’re going to notice this sort of the equation

that we have b on both of these,

so we can put a b here

and if I divide b into… ab here, I get a

and if I divide b into b² here, I get to be here.

Okay so, this is where this has been factorized.

The next thing I’m gonna do is I am going to

divide both of these sides by the common factor

which is a take away b we can divide

I’ll put that in brackets a take away b.

So, what are you do that and see what you get

if you divide this side by a take away b,

you’re going to get a plus b

and on this side if you divide by a take away b,

you’re going to get b.

Alright, so what do we know?

We know that a is equal to b.

So if a is equal to b, I could say a here is b.

Okay? They’re the same thing a is equal to b

so I’m gonna substitute b for a.

So b plus b is equal to b,

that means 2b is equal to b

and if you now divide both sides by b, what do you get?

You’re gonna get this proof here

that indeed 2 is equal to 1. Proven!

Hey, what do you think of that, all right?

I can prove it! I have found the impossible!

I have shown that 2 is equal to 1.

Okay, but is it true?

And straight away you’re gonna know intuitively

that 2 is not equal to 1.
2是不等于1的
Of course, 2 is not equal to 1.

So why don’t you go through here and

see where I have made a bit of a fallacy, a bit of an error,

a bit of a sneaky sort of bit amounts.

So pause it see if we can go through and find it.

Okay, did you find out where that was?

Alright. I’ll give you a bit of a hint of what’s going on here.

It’s what’s now an asset division by zero fallacy, okay?

Somewhere along here we have divided by zero

and as you know you can’t divide by zero, yeah that’s not possible.

You do that on a calculator you getting there error.

Okay you can’t divide by zero.

The universe just does not like that, okay?

You can’t see how many nothings are in something.

It just doesn’t make sense.

So where do we divide by zero here?

At this step we multiply by a,

so we didn’t divide by zero.

And this step we took away b², okay?

This one we factorize

and we just rearrange the equation.

This one we divided by a take away b.

We did divide here

but did we divide by zero?

Well, let’s substitute in our values here and we’ll find out.

So we’ve divided by…

and a is equal to 1
a是等于1的
and B is equal to 1.
b是等于1的
So 1 take away 1

and if you have a look here

that means we’re divided by zero at this step.

As we go from this step to this step,

we’re divided by zero.

And that’s caused what’s known as a division by zero fallacy.

Interesting, good for tricking people,

but also something that you want to watch here for when you’re doing maths okay?

if you’re playing around with algebra or anything like this,

it’s a really really common easy mistake to make.

There’s a few little fallacies, a few little mistakes

that people make when they’re doing algebra

and so this is one of the reasons I’m showing you this video,

not just because it’s a boy’s phone I’m a little bit fun

but also I think it’s a it’s a good thing to know

because then you know to watch out for it okay

and you know it’s a source of error.

So tell us what you thought of that, okay?

Uh… anyway great to be making videos.

See you next time, bye.

HiyaTay