Why can't you divide by zero? - Free Educational videos for Students in K-12

Why can't you divide by zero? - By tecmath

Transcript


00:0-1	Good day . Welcome to Tech Math channel . What
00:01	we're gonna have to look at in this video is
00:03	division by zero . Okay . This is there in
00:05	response to a video I made last week and I
00:09	said incorrectly that if you divide by zero , we
00:12	couldn't do it because we get nothing . And I
00:16	quite correctly got picked up by a bunch of commentators
00:19	with this , which I thank you for you .
00:20	Going to see some of the comments down below .
00:21	Um , so I'm going to in this video address
00:25	why you can't divide by zero ? What's the go
00:27	with that ? So let's launch into this . So
00:29	I'm going to start out this investigation by just considering
00:32	one divided by zero and the different answers that people
00:36	tend to get or give me if I've ever asked
00:38	this question . Now there's three major types of answers
00:41	I hear with this . Apart from me , I've
00:43	got no idea which is this ? The first one
00:46	is a lot of people . This is the vast
00:47	majority tend to say there is no zeros in one
00:51	. Okay , The one divided by zero is zero
00:54	because there's no zeros in one at all . The
00:57	next most popular answer I've also heard is probably this
01:00	one , Is that the answer is infinite ? Okay
01:03	, if you're gonna go one divided by zero ,
01:05	that the number is so huge that it's an infinite
01:08	answer , the next type of answer I've heard is
01:11	this one ? Is that the answer is undefined ?
01:15	Okay , now I'm going to tell you straight away
01:18	that the actual answer is that dividing by zero ?
01:21	The answer is undefined , but I'm going to show
01:23	you now why this is the case . So let's
01:25	start with something . We do know the answer .
01:27	I think all of you know the answer to which
01:28	is one divided by one , which you know is
01:30	to be one . What I'm gonna do is I'm
01:33	gonna slowly start Messing around this number here and making
01:37	an approach zero and we're going to see what happens
01:39	to the answer . So if I was to go
01:42	one divided by 0.1 , You're gonna see . Okay
01:46	, what's my answer here ? That's 10 . And
01:49	the next thing I'm gonna do is I'm going to
01:50	make this a little bit smaller . Now , I'm
01:51	gonna go one divided by point 01 This is equal
01:55	to 100 . You're going to notice what's happening .
01:57	This number is getting bigger on this air . Answer
02:00	is getting bigger is this number we're dividing by approaches
02:03	. You don't get smaller . This answer here is
02:05	getting bigger . Let's go one more . What about
02:08	if I go one divided by 0.001 ? Well ,
02:12	again , it's going to be 1000 . And you
02:16	can probably guess is this number here approaches zero .
02:19	This number here gets really big as this number here
02:21	gets infinitely small and approaches zero . This number here
02:25	gets infinitely large . So it seems quite intuitive that
02:28	you can actually say to one approach to zero or
02:32	one divided by zero . Perhaps people could actually say
02:36	, but this is equal to infinity . But I'm
02:39	gonna tell you right now that this leads to a
02:40	few problems . So say that I was to say
02:43	the instead what is too divided by zero ? Okay
02:48	, two divided by zero . Start with two divided
02:50	by one . I get the answer of two and
02:52	then I go to the next one . I go
02:53	to divided by 0.1 and I get 20 And I
02:57	go to divided by a 0.01 and I get 200
03:03	and the same sort of thing . Eventually go down
03:05	. And I could start to get this sort of
03:07	thing where two divided by zero , given this idea
03:10	would also equal infinity . But do you see a
03:13	problem here , infinity ? An infinity ? These guys
03:17	here equaling one another or maybe then I can start
03:19	to say , okay , well these both equal infinity
03:23	, 1/0 equals 2/0 . And I cancel out the
03:26	zeros , and I could say two equals one .
03:28	And I've got a real problem here , not to
03:31	also mention the fact that infinity is not really a
03:34	number of answers . So it's kind of messy .
03:37	It's kind of horrible , but I'll show you the
03:39	other uh problem that we have with this and that's
03:41	this when we're doing this particular thing , we're approaching
03:44	zero from the positive side , but say we were
03:47	to do the opposite , and we want to approach
03:49	zero from the negative sort , So you go one
03:53	Divided by -1 , and we get this answer of
03:57	negative one and then I can go the next one
03:59	and I can make this smaller and approach zero from
04:01	the negative side . And I could go one divided
04:04	by negative 0.1 . And I'm gonna get this answer
04:07	of negative 10 and the next one like it goes
04:10	one divided by negative 0.01 and this is equal to
04:15	negative 100 . So you're gonna probably get this idea
04:18	I go one more one divided by negative 0.1 That
04:23	this is gonna be negative 1000 UK will okay .
04:27	Perhaps what we have is we go and we're still
04:29	approaching zero but now from the negative side , maybe
04:32	we do this we get one divided by zero because
04:35	we're approaching it from the negative side and we're getting
04:38	negative . Infinitive is our answer . And so you
04:41	see a bit of a problem here straight away ,
04:44	if we approach zero from this side , we're dividing
04:46	by zero , we're getting infinity . And in this
04:48	one we're getting negative infinity in there and we have
04:51	to complete difference of standpoints here that are equally as
04:54	valid if we use this particular idea . And because
04:58	of this , this is why one divided by zero
05:02	is said to be undefined . It's not infinity because
05:05	I could equally say , well it's negative infinity .
05:08	So one divided by zero is said to be undefined
05:12	, and I could leave it there , but I
05:14	just want to show you one more thing . And
05:17	the thing that I want to show you is this
05:20	zero divided by zero . Just leads a little bit
05:23	of extra complication of this . Now , I can
05:26	imagine that you'd start with you no one here .
05:28	And you can say , okay , I'm going to
05:30	divide it up as many times as I can ,
05:32	and you can't start cutting off nothing , cutting off
05:34	nothing , cutting off nothing , this is your one
05:36	here , but you never get anywhere . And so
05:38	, you know , I could , you could definitely
05:41	say uh you know , you can get a conceptual
05:43	that this is , you know , because of what
05:45	we've already gone through , this is undefined , it's
05:47	either infinity or negative infinity , but it becomes undefined
05:50	because it's undefinable . But this sort of idea becomes
05:53	a bit of a problem because what we have is
05:56	we have a number that divides by itself . And
05:59	straight away you might be able to say , well
06:01	, ok , any number divided by itself is one
06:04	, so maybe zero divided by zero is one .
06:07	And you can also look and say zero divided by
06:10	any number gives us an answer of possibly zero .
06:15	Or what you could say is that we have an
06:17	answer . Once again that is undefined , so which
06:22	one is it ? And I just want to explain
06:24	this to you because I think it gives us a
06:25	greater understanding in this division by zero problem . So
06:29	which one of these is it ? I'll tell you
06:30	straight away . Once again , zero divided by zero
06:34	is undefined , and I'll show you why this is
06:37	oh and to do this , I'm going to show
06:39	you using multiplication . Because imagine this because we do
06:43	know that division is the inverse operation of multiplication .
06:47	What I'm gonna do is I'm gonna say okay what
06:49	zero times one , and you're gonna say okay zero
06:52	times one is zero and zero times too , and
06:56	that's also zero . In fact zero times any number
07:01	is equal to zero . So let's do the inverse
07:04	of this multiplication and see what we get . So
07:07	I'll change colours . Uh and what I'm gonna do
07:10	is I'm and instead go zero divided by zero .
07:14	And if this is the case , it should be
07:16	equal to one Or zero , divided by zero .
07:21	Could be equal to two or 0 , divided by
07:24	zero could be equal to any number . So it's
07:28	a bit of a thing that we actually we can't
07:31	define zero , divided by zero to anything . It
07:34	could be one . It could be too because of
07:35	this idea of the inverse operation , this this could
07:38	go anywhere . So not only could be infinity or
07:41	negative infinity , we could almost be anything . And
07:44	this is the reason that we actually are say it's
07:47	undefined anyway . I hope that's clear up a few
07:50	things . I am going to guarantee I'm going to
07:52	have a bunch of unhappy people in a common section
07:55	below . I'm sure I've made a little error there
07:58	somewhere that somebody wants to pick me up . That's
08:01	all right . We'll keep the discussion going on this
08:03	. I reckon it's a really , really positive thing
08:05	anyway . Thanks for watching . We'll see you next
08:08	time . Bye . And just finally , the Tech
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