You can assign each rational number a single unique integer though if you use a simple algorithm. So the 1:1 correspondence holds up (though both are still infinite)

For every integer, there are an infinite number of real numbers until the next integer. So you can’t make a 1:1 correspondence. They’re both infinite, but this shows that the reals are more infinite. (and yeah, as other people mentioned, it’s the 1:1 correspondence, countability, that matters more than the infinite quantity of the Real numbers)

Thank goodness that last pic is edited, the bird didn’t fall did it? (not ironic, I got worried about the bird and want a happy ending here)