Proof that 2+2=5....How math can lie - Free Educational videos for Students in K-12

Proof that 2+2=5....How math can lie - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Mouth channel . What
00:01	we're gonna be having to get in this video is
00:03	another false proof . Where I am going to show
00:04	you this time . The following that too . Plus
00:08	two is equal to five . Okay , So obviously
00:13	, you know the two plus two dozen equal five
00:15	. So probably what I would really , really hope
00:17	for you in this video is you're trying to spot
00:19	where I insert the lie . Okay , So ,
00:21	uh , let's do this . I'll get rid of
00:23	that . Give us a bit of space . So
00:25	, I'm gonna start out with the following idea that
00:27	we have negative 20 and it's equal to negative 20
00:33	. Okay , pretty good . So far nothing wrong
00:35	here . The next thing I do is I am
00:37	going to change these around basically . So we have
00:41	two equivalents of -20 . The first one on this
00:44	side , this is going to be 25 . Take
00:48	away 45 . Okay , 25 take away 45 is
00:52	negative 20 and this one here is going to be
00:55	16 Take away 36 . All right . The next
01:00	thing I'm going to do is I am going to
01:03	rewrite these a little bit because 25 is equal to
01:06	five squared and -45 is equal to negative five times
01:12	nine , 16 can be written as four squared and
01:18	negative 36 can be written as negative four , multiplied
01:23	by nine . All right . Nothing wrong . So
01:26	far right . The next thing I'm gonna do is
01:28	I am going to add 81/4 to both sides .
01:33	Like I'm going to add 81/4 to both sides .
01:36	So this Side of the equation , if I do
01:39	that is going to equal five squared -5 times nine
01:45	Plus 81/4 . And this side to keep it nice
01:50	and balanced . I'm going to do the same thing
01:52	. This is going to equal four squared what is
01:55	four Times nine plus that same amount , 81/4 .
02:01	Now I want to do is I am going to
02:03	factories this equation , I'm going to put it in
02:06	brackets . Uh I get the following , I am
02:08	going to get 5 -9 over to and this is
02:12	squared and this is equal to 4 -9 over to
02:19	and this is squared . Alright . I don't know
02:21	if you've seen a problem yet to this sides .
02:23	Now , what ? Both sides ? I am going
02:24	to square root and we have this squared , we
02:26	have this squared , this is equal to this squared
02:28	. So basically would make sense if I was to
02:31	say , okay , I'm going to square root these
02:33	, this is five minus nine over to And this
02:37	is equal to 4 -9 over to . Ah Then
02:42	what I'm gonna do is I can cancel out both
02:45	of these . I can cancel out the nine ,
02:47	negative 9/2 . And I can cancel out this negative
02:49	9/2 by adding nine over to to both sides .
02:52	And if I do that , I am going to
02:54	end up with five equals four . And this as
02:59	you know , is equal to two plus two .
03:01	So two plus two Is equal to five . All
03:05	right . So , did you spot where the are
03:09	lie was inserted there ? Where the problem was ?
03:13	Go through my working out . See if you can
03:14	spot it . Okay . I will tell you where
03:20	this lie was where the fallacy was right now .
03:23	So , the fallacy that was inserted is to do
03:25	with positive and negative roots . Okay . And what
03:28	this means is this basically at this stage , at
03:31	this particular stage here . This is where the problem
03:34	is where I go from this step to this step
03:37	and or square root . And what I have here
03:39	is I have this squared being equal to the square
03:42	here . I'm going to represent that here as a
03:44	squared being equal to be squared OK . This squared
03:49	A squared is equal to be square . This one
03:51	here , the problem that I have here is it's
03:53	only true if A is equal to negative B .
03:58	Okay , So basically what this is saying is you
04:01	have to be very , very careful occasionally when you
04:03	are taking the square root of both sides of the
04:05	equality and if you don't do it correctly , what
04:08	you can end up with is a false proof .
04:10	So this particular step here , we've assumed that basically
04:14	I've taken it down , so this has become positive
04:16	and this has become positive , you know , equals
04:18	B . And everything is good in the world ,
04:20	right ? But this is not the case . I'll
04:21	show you the alternative that would occur . If I
04:24	assume that A is equal to negative be at this
04:27	particular step here , what would occur would be this
04:30	? I'm just going to move it up a little
04:32	bit just to give ourselves a bit of space .
04:34	So if I'm saying that equals negative B , well
04:37	at this particular step , as I went from here
04:39	to here , I would have 5 -9 over to
04:44	okay as I square rooted it and this would be
04:47	equal to instead of Just being 4 -9 over to
04:51	this is going to be negative and I'll put that
04:54	in brackets here , 4 -9 over to Okay ,
04:57	that's annoying there . And if I was to do
05:00	this , I'll expand this out now , this would
05:03	be equal to okay , this is going to stay
05:04	as 5 -9 over to . This would become equal
05:07	to negative for minus times minus is a positive .
05:11	So plus nine over to give myself a bit more
05:14	space now . Both these sides , what I'm gonna
05:18	do is I'm going to get rid of this 9/2
05:21	by adding nine over to to both sides . Five
05:24	is equal to because I add nine over to us
05:27	, it's going to counsel it out . This is
05:28	gonna be negative for plus nine over to Plus nine
05:33	over to and just a bit more space . So
05:39	this is going to be equal to so five is
05:40	going to be equal to minus four which is plus
05:44	9/2 plus 9/2 . So the minus 4 , 9/2
05:48	plus 9/2 , that's 9.5 of nine plus half of
05:51	nine , which is going to be equal to nine
05:54	. And then what would have is five is equal
05:56	to five . And this would be correct . And
05:58	so as you see here , this is one of
06:02	these types of fallacies where this squaring only the square
06:06	rooting here only works if we we know that A
06:10	. Is equal to negative B . Okay . So
06:12	it's a squaring fallacy square rooting fallacy . Anyway ,
06:17	another type of our proof here . So just another
06:19	thing to be careful of Once again , I think
06:21	there's a really , really good because you know ,
06:23	they show you what to look out for when you
06:25	are actually doing various operations in maths . So tell
06:28	us what you think of that one . A little
06:29	bit messier . This one . Okay . But I
06:31	think a really , really valuable one to look out
06:33	for . Tell us in the comments section , what
06:35	you think uh fly me if you want Anyway ,
06:40	see you next time . Bye . And just finally
06:44	, the Tech Math Channel has merchandising . So click
06:48	on the link . You're gonna see below the video
06:50	going off the T spring there . Ah you know
06:52	, we got cups where you got shirts , we
06:54	got hoodies . I can guarantee you where these you
06:56	will be at least the 12th coolest person on the
06:59	street . So click on the T Spring link below
07:01	to get to the Tech Math merch store .

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Proof that 2+2=5....How math can lie is a free educational video by tecmath.

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