Prove me wrong

For students of class 11-12 (age 16+)
tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am
Location: Pasadena, California, U.S.A.

Re: Prove me wrong

Unread post by tanvirab » Mon Dec 26, 2011 3:34 pm

Masum wrote: may we define it some other way?
Sure. that's what I have asked probably 20 times in this thread. What is the definition of $0/0$? Define it.

raihan khan
Posts: 35
Joined: Wed Mar 16, 2011 12:30 pm
Location: Dhaka

Re: Prove me wrong

Unread post by raihan khan » Tue Jan 03, 2012 10:16 pm

1/0 is never infinity lim x tends to zero 1/x is infinity. zafar sir said that by numerical method.if you set a number that is very nearly o from the left side of the number line it would be a left hand limit and if you set from the right side it would be right hand limit. the expression is
lim 1/x = infinity lim 1/x = - infinity
x tends to o+ x tends to 0-

User avatar
Masum
Posts: 592
Joined: Tue Dec 07, 2010 1:12 pm
Location: Dhaka,Bangladesh

Re: Prove me wrong

Unread post by Masum » Tue Jan 03, 2012 11:28 pm

raihan khan wrote:1/0 is never infinity lim x tends to zero 1/x is infinity. zafar sir said that by numerical method.if you set a number that is very nearly o from the left side of the number line it would be a left hand limit and if you set from the right side it would be right hand limit. the expression is
lim 1/x = infinity lim 1/x = - infinity
x tends to o+ x tends to 0-
I think the logic that was represented by Sir, is not strong enough to explain this. Sir just said that when we approach from both positive and negative end, we approach infinity but what if it is exactly $0$? The answer he said is "it is not possible to reach $\frac10$" but there is the problem. He didn't explain why so was. So I am not satisfied at all with this explanation. This does not make any sense to me.
One one thing is neutral in the universe, that is $0$.

tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am
Location: Pasadena, California, U.S.A.

Re: Prove me wrong

Unread post by tanvirab » Wed Jan 04, 2012 1:08 am

Masum wrote: "it is not possible to reach $\frac10$"
because that is not defined. You cannot talk about something that is not defined. So reaching $0$ in that limit would not make any sense.
In any case, "limit" does not mean you reach anything. Look at the definition of limit. You never have to reach anything, it just says about going close to things.

User avatar
Masum
Posts: 592
Joined: Tue Dec 07, 2010 1:12 pm
Location: Dhaka,Bangladesh

Re: Prove me wrong

Unread post by Masum » Wed Jan 04, 2012 11:21 am

tanvirab wrote:
Masum wrote: "it is not possible to reach $\frac10$"
because that is not defined. You cannot talk about something that is not defined. So reaching $0$ in that limit would not make any sense.
In any case, "limit" does not mean you reach anything. Look at the definition of limit. You never have to reach anything, it just says about going close to things.
My point was the same. Well, I didn't argue about the definition or $\frac10$ is defined or something like that? But you can't say just after saying that we approach from both end, and say that $\frac10$ is undefined, how can it make sense?
One one thing is neutral in the universe, that is $0$.

tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am
Location: Pasadena, California, U.S.A.

Re: Prove me wrong

Unread post by tanvirab » Wed Jan 04, 2012 3:23 pm

$1/0$ is undefined because it has not been defined. That has no connection with limit.

User avatar
Masum
Posts: 592
Joined: Tue Dec 07, 2010 1:12 pm
Location: Dhaka,Bangladesh

Re: Prove me wrong

Unread post by Masum » Wed Jan 04, 2012 10:55 pm

Oh again, the definition!! Who told them about this? I told about the explanation of Sir! Agartala is not Amtala, right? You are saying this just because you yourself can make an explanation with the help of definition. But can you convince a primary student with this explanation of Zafar Sir? Why are you mixing up things? That is complete non-sense.
One one thing is neutral in the universe, that is $0$.

tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am
Location: Pasadena, California, U.S.A.

Re: Prove me wrong

Unread post by tanvirab » Wed Jan 04, 2012 11:50 pm

Masum wrote:Oh again, the definition!! Who told them about this? I told about the explanation of Sir! Agartala is not Amtala, right? You are saying this just because you yourself can make an explanation with the help of definition. But can you convince a primary student with this explanation of Zafar Sir? Why are you mixing up things? That is complete non-sense.
What are you talking about? I though the question was why we cannot reach $1/0$?

tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am
Location: Pasadena, California, U.S.A.

Re: Prove me wrong

Unread post by tanvirab » Thu Jan 05, 2012 12:00 am

BTW, Zafar Iqbal's explanation is wrong. In the most common definition of infinity, there is no such things as positive/negative infinity. They are all the same. It's called one-point compactification (the one-point is infinity).

tanvirab
Posts: 446
Joined: Tue Dec 07, 2010 2:08 am
Location: Pasadena, California, U.S.A.

Re: Prove me wrong

Unread post by tanvirab » Thu Jan 05, 2012 12:17 am

Zafar Iqbal's explanation is correct to show that the limit does not exist in real numbers. Because from one-side the limit has to be positive and from the other side it has to be negative. But this explanation cannot be use to say what the limit is (i.e. infinity) or what $1/0$ is. For those you will have to go back to definitions. There are a few ways to define infinity, the most common is one-point compactification, as I mentioned. There are no ways to define $1/0$ so far.

Post Reply