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Masum bhai, what do u think about $0/0$ ...

What makes the sense to me is: Do what we always do naturally. Let $\frac00=k\in\mathbb R$ because when we reach a state contradicting a definition, we stop there. So, let us proceed until we find that contradiction to our definitions, then according to the rules of real numbers, we get \[0=k\cdot0\]
Now according to the definition(not exactly contradiction, but conclusion) of $0$(because everything that comes about definition is after the definition of $0$) the equation is true for all $k\in\mathbb R$. Thus we can't exactly say what the value is. Therefore, my conclusion is it is undeterminable.

Masum wrote: Let $\frac00=k\in\mathbb R$

The point I am trying to establisg is that this (the above) makes no sense. What is $\frac{0}{0}$? If you cannot define it then saying that it's in real is nonsense. For $0/0$ to make sense you first need to define the division of zero by zero.

For example if I say $3@4 \in \mathbb{R}$, what does it mean? Nothing. Because I have not defined what $@$ means. Division also needs to be defined in the same way. You cannot just say something that's not defined.

tanvirab wrote:
The point I am trying to establish is that this (the above) makes no sense. What is <span class="math">\frac{0}{0}</span>? If you cannot define it then saying that it's in real is nonsense. For <span class="math">0/0</span> to make sense you first need to define the division of zero by zero.

Not exactly what I meant. You are saying about the definition but we need argument to conclude something. You need to provide some argument before conclusion of-course. But when you say that now define $\frac00$ in the same way doesn't make the sense why it can't be. But still I need to know when do we say something defined, may be well-defined? And I guess that you are claiming this because of $\frac10$. But in real why should $\frac00$ be dependent on $\frac10$.
For example, let $a@b$ be $\frac{ab+a+b}b$. Then before any arguments could you say that $3@0$ is undefined? Does it make sense or sound better?

No. You still need to define $0/0$ before making arguments about it. What is $0/0$?

Just to make it clear, when you say something about something you need to know what that things is i.e. you need to define it.

For example when I say $3/4$ I can define it, but when I say $3@4$ that does not mean anything, because I have not defined it. When I say $0+0$ I can define it, but no one has so far defined $0/0$. So, before even starting to talk about $0/0$ you need to say what it is. What is $0/0$?

Masum wrote: Let $\frac00=k\in\mathbb R$

In other words, all of your argument is based on this assumption. But who told you that this assumption is true? No one. Because it is not true. You cannot assume something that is not true and then make arguments based on that. For any of your arguments to make any sense, you first need to prove that this assumption is true. Is it true?

tanvirab wrote:

Masum wrote: Let $\frac00=k\in\mathbb R$

In other words, all of your argument is based on this assumption. But who told you that this assumption is true? No one. Because it is not true. You cannot assume something that is not true and then make arguments based on that. For any of your arguments to make any sense, you first need to prove that this assumption is true. Is it true?

Who said that it is not true? At least no one can sense them Then when shall you say that is false. After some kinds of stuffs I used. Isn't it?Otherwise, how can you expect to have them proved.

tanvirab wrote:Just to make it clear, when you say something about something you need to know what that things is i.e. you need to define it.

For example when I say $3/4$ I can define it, but when I say $3@4$ that does not mean anything, because I have not defined it. When I say $0+0$ I can define it, but no one has so far defined $0/0$. So, before even starting to talk about $0/0$ you need to say what it is. What is $0/0$?

Actually I wanted to explain it only using the definition I gave. Then how shall you conclude that $3@0$ defined or undefined?