A decades long lurker on this site I'd like to say thanks for starting this thread, I'm really enjoying excercising the old grey matter on some of these.
However, I would respectfully disagree with your assertion that "You can't have .... different size infinities"
For example: the set of all integers and the set of even integers are both infinite. But for every member of the second set there are two members of the first set. So both sets are infinite in size - but one is twice as big as the other
I don't suggest thinking about this stuff too much though as it is known to drive people mad ( https://www.bbvaopenmind.com/en/science/mathematics/georg-cantor-the-man-who-discovered-different-infinities/ )
Blimey - I never expected to be discussing Cantor's set theory on a rugby league website! Just goes to show we really are the superior code