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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