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#1 Re: Help Me ! » Undefined And Indeterminate » 2015-01-20 06:04:26
Hello Bob!
But now you want (0/0).x = (0.x)/0 Can you switch about the brackets like this?
Yes! Right?
So (0.x)/0 = kx => 0/0 = kx => kx = k => x = 1 which is a contradiction.
So one of your steps / assumptions is wrong. Maybe it is that 0/0 is indeterminate. I'd accept that.
Okay , Let x be any real number other than 1.
Have you done any calculus yet ?
The differential calculus is founded in the idea that we can, for certain functions, find a value for 0/0 .
So a lot of mathematicians are going to be very unhappy if 0/0 is undefined.
Yes , I have studied calculus. But I have got a bad teacher ( I think so ). He says that (->0)/(->0) is indeterminate
( Shouldn't it be 1 always? ).
#2 Re: Help Me ! » Undefined And Indeterminate » 2015-01-20 02:33:00
Hello Bob!
I don't think the Khan Academy guy is assuming that y/y = 1.
If he didn't assume y/y = 1 then how does he get x * (y/y) = x ?
I'm confused about whether you are then offering an improved proof. If you are, please post just that again and I'll give it some thought.
The improved proof I was offering was this ( The proof which I am giving is to prove that 0/0 is indeterminate ):
Let 0/0 = k. (k is any real number)
Now , we will multiply both sides by any real number x ( which can also be zero )
LHS = (0*x)/0 = 0/0. But RHS = k*x = any other real number. Therefore 0/0 is indeterminate , i.e ., it can be any
real number.
I am now suddenly getting a doubt.
Shouldn't 0/0 stay undefined?
If 0/0 = a (any real number). Also 0/0 = b (any other real number) . Therefore a = b , but a =/= b!
It is violating the equality sign!
Please clarify me regarding this. I think it is better for 0/0 to stay undefined to remove these confusions!
Thanks for your reply!
By the way I liked your argument/proof on why x/0 ( x not equal to zero ) should stay undefined. I am now satisfied
on why x/0 should stay undefined.
#3 Re: Help Me ! » Undefined And Indeterminate » 2015-01-20 00:28:55
Hello Bob!
The step ( given below ) which you have done from multiplication to division requires that you divide both sides by 'b' , right?
If a times b = c, then you can define division as c/b = a.
This is the process I posted in my question and for this to be valid , b/b has to be 1.
The process I am talking about :
Process : 0/0 = k
0*(0/0) = k*0
0*1 = k*0
0 = k*0
The problem is by doing this process we assume that 0/0=1 and then prove that 0/0 is indeterminate. So , isn't it wrong?
Thanks for your reply and please forgive me if I am annoying.
#4 Help Me ! » Undefined And Indeterminate » 2015-01-19 20:41:47
- Ajay Mohan
- Replies: 7
Hello people!
I have recently seen a video on khan academy about why we can't define a number to any number divided by 0 ( except 0 ) and why 0/0 is indeterminate.
I have found something wrong with this video. I posted a query but never got a reply.
Problem I :
At 1:00 , he writes an identity which is x*y/y = x.
The problem is that he hasn't specified the values which 'y' can take.
Case I : If y can be any real number including zero , then he indirectly implies that 0/0 is always one , which
contradicts when he says 0/0 is indeterminate.
Case II : If y can be any real number except zero , he cannot use this identity at 3:00 where he uses this identity for
y = 0.
After being confused , I came to MIF website and while explaining why x/0 is undefined while x not equal to zero , they consider the case when x=0 and say it is undefined.
-----> Is it possible to prove that x/0 is undefined when x is not equal to zero without bring 0/0?
Problem II :
Even in the last part of video , when he is trying to prove that 0/0 is indeterminate , he transfers the zero from denominator in LHS to numerator in RHS which would work on normal numbers. A brief working tells that we have to assume 0/0 is one in the process.
Process : 0/0 = k
0*(0/0) = k*0
0*1 = k*0
0 = k*0
----->Also , Can someone say if my idea regarding why 0/0 is indeterminate?
Let 0/0 = k . Now , we can multiply both sides by any real number including zero.
(0*x)/0=0/0. But the RHS has changed which is k*x. Therefore , it can have many values and it is indeterminate.
#5 Introductions » Greetings everybody! » 2015-01-18 03:45:50
- Ajay Mohan
- Replies: 6
Hello to everyone on this forum.
My name is Ajay and I live in India. I started to love this website since I started reading the concept on limits and infinity. It was very beautifully explained! A major reason I registered in this forum was to thank the people who explained everything in a clear manner. The thing about maths is that when you realize the beauty of it , you would try to explain it to others to give them the joy which you had!
I hope I can some friends on this forum who think of maths just as I do.
Thanks for reading!
P.S : Where can I post my doubts in this forum so that other people can clarify it?
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