I saw that thing that if you biject set of all the natural numbers and a set of all the even numbers, they are able to pair. I don't think you can compare two infinites just like this I believe there's still a way to solve it better.
My solution is: Let $E$ be all the even numbers. Let $O$ be all the odd numbers. If you put together the even numbers and the odd numbers, this is called the natural numbers.
Now what need to do is biject between $E\cup O$ and $E$, what that happens is that $E$ is removed and what is left is $O$ and nothing. Isn't it means that they don't biject?
What I want to know is that why I am wrong.