Trick your math teacher - Free Educational videos for Students in K-12

Trick your math teacher - By tecmath

Transcript


00:01	get a welcome to the Tech Math channel . What
00:03	we're gonna be doing this video is I'm going to
00:04	prove to you that two is equal to one .
00:08	Okay ? So you might be thinking there's no way
00:12	he can prove this . But sit back . I'll
00:13	show you . All right . The first thing I'm
00:16	gonna do is I'm going to use two letters to
00:18	do this . They're gonna be A and B .
00:20	Here . And we're going to say that these guys
00:22	are equal to one another . So they could be
00:24	equal to one . B . Could be equal to
00:25	one . All right . So let's start off with
00:28	this . We're going to say that A is equal
00:30	to be All right . I think we can agree
00:32	on that one . Yeah . The first thing I
00:34	do this equation is I am going to multiply it
00:37	by A . So if we were to do this
00:39	eight times A is A squared and A times B
00:45	is a B . Now to both sides . What
00:48	we're going to do is we're going to take away
00:51	B squared . So , maybe you want to do
00:53	that and see what we get . If you get
00:55	a square and take away B squared , you're gonna
00:57	get a squared take away B squared . And this
01:01	site , you're going to get a job take away
01:05	B squared . The next thing I'm going to do
01:09	, we're going to get you to do is we
01:11	are going to factories this . Okay ? We're gonna
01:13	factories this . All right . Maybe you can give
01:17	an attempt doing this . What you'll notice is this
01:18	is a difference between two squares here . So ,
01:21	a squared take away be square becomes the following .
01:25	It becomes a takeaway be and A plus B .
01:29	And if you don't believe that expanded out , that's
01:32	what this becomes here . This one here . You're
01:35	going to notice this side of the equation that we
01:37	have a B on both of these . so we
01:38	can put a B . Here . And if I
01:41	divide be into A B . Here , I get
01:44	A . If I divide being to be squared here
01:46	are going to be here . Okay , So this
01:49	is where this has been fact arised . The next
01:52	thing I'm going to do is I'm going to divide
01:55	both of these sides by the common factor , which
01:57	is a takeaway be we can't divide . I'll put
02:00	that in brackets , A takeaway be . So why
02:04	don't you do that and see what you get ?
02:06	If you divide this side by a takeaway , be
02:07	you're going to get a plus B . And on
02:12	this side of you divide by a takeaway be you're
02:14	going to get B . All right , So ,
02:17	what do we know ? We know that is equal
02:19	to be ? So , if A is equal to
02:21	be , I could say a here is B .
02:24	Okay . They're the same thing is equal to be
02:26	so I'm going to substitute be for a B plus
02:29	B is equal to be . That means to be
02:34	is equal to be . And if you now divide
02:38	both sides by B , what do you get ?
02:40	You're going to get this proof of that ? Indeed
02:44	. Two is equal to one proven . Hey ,
02:49	what do you think of that ? All right ,
02:50	Okay . I've proven that I have done the impossible
02:52	. I have shown that two is equal to one
02:55	. Okay , But is it true ? And straight
02:57	away you're gonna know intuitively that too is not equal
03:00	to one . Of course to is not equal to
03:01	one . So why don't you go through here and
03:03	see where I have made a bit of a fallacy
03:07	? A bit of an error . A bit of
03:08	a sneaky sort of bit of matt . Suppose it
03:11	see if we can go through and find it .
03:14	Okay . Did you find out where that was ?
03:17	All right ? I'm gonna give you a bit of
03:19	a hint what's going on here ? It's what's known
03:21	as a division by zero . Fallacy . Okay .
03:24	Somewhere along here we have divided by zero . And
03:26	as you know , you can't divide by zero and
03:28	it's not possible . You do that on a calculator
03:31	. Getting that error . Okay . You can't divide
03:33	by zero . The universe . Just does not like
03:35	that . Okay . You can't see how many nothing's
03:37	are in something . It just doesn't make sense .
03:39	So where do we divide by zero here ? At
03:43	this step we multiplied by a so we didn't divide
03:45	by zero at this step we took away B squared
03:48	. Ok . This one we factories and we just
03:50	rearrange the equation . This one we divided by a
03:54	takeaway be So we did divide here . But did
03:57	we divide by zero ? Well let's substitute in our
03:59	values here and we'll find out . So we've divided
04:02	by and R . is equal to one and B
04:07	is equal to one . So one take away one
04:09	. And if you have a look here , that
04:11	means we're divided by zero at this step . As
04:14	we go on from this step to this step were
04:16	divided by zero . And that's caused what's known as
04:19	a division by zero fallacy , interesting . Good for
04:22	tricking people , but also something that you want to
04:24	watch out for when you're doing your maths . Okay
04:26	, if you're playing around with algebra or anything like
04:28	this , it's a really really common , easy mistake
04:31	to make . There's a few little fallacies , a
04:33	few little mistakes that people make when they're doing algebra
04:36	. And so this is one of the reasons I'm
04:38	showing you this video , not just because it's a
04:40	I've always found him a little bit fun , but
04:42	also I think it's , um , it's a good
04:44	thing to know because then , you know , to
04:45	watch out for it . Okay ? And you know
04:47	, that's a source of error . So tell us
04:49	what you thought of that . Okay , Anyway ,
04:52	great to be making videos . See you next time
04:55	. Bye .

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