[![enter image description here](https://i.stack.imgur.com/Kscpq.png)](https://i.stack.imgur.com/Kscpq.png)

The function $f(k) = \mathbb{N}^k$ is a one to one function but it is not an onto function. Hence the function is not a one to one correspondence function. 

Does that give sufficient justification to proof that the given set in not countable? Or is there any other way to approach the same.