A convergent Double Sequence will be bounded also.
My Attempt: I think the statement is not true.
Counter Example : $a_{1n} = n$, $ a_{mn} = 1/m + 1/n$ for all $m \geq 2$
lim$_{m,n \to \infty} a_{mn} =0$ But $ a_{mn}$ is not bounded .
Have I gone wrong anywhere? Can anyone please help me?