Things quickly fall apart if you rely on your intuition.

Let's imagine all the odd numbers: 1, 3, 5, etc. Now imagine all the even numbers: 2, 4, 6, etc.

Can we agree that there is an "infinite" amount of numbers in each of those groups?

Now imagine all the odd numbers and even numbers together. That's also infinite right?

Would you say there are more "all numbers" than just "all odd numbers", or would you say that there are an equal number of them? (hint: the answer is equal).