What is $0 \times \infty$? My question is - I know, $0\times anything=0$ and $anything \times \infty=\infty$.
So,what is $0 \times \infty$?
I suppose it's $0$ but why not $\infty$?
If I say that area of an indefinitely long line is $\infty*0=0$,where am I wrong?
I know upto limits and basic derivatives.
Thanks.

Here's a simple example.
The product $0 \times \infty$ is what we like to call an indeterminate form because at first glance and without limit analysis, we cannot find a solution.


*

*$10^{-100} \times 10^{10}$ is going to be a very small number multiplied by a very big number. The answer is $10^{-90}$ which is a very small number (close to 0)

*$10^{-10} \times 10^{100}$ is also a very small number multiplied by a very big number but the answer, unlike in the previous example, is $10^{90}$ which is a very big number.
