[hcarlens]

Good try, and there are indeed different types of infinities, but your examples both represent the same "countable" infinity of the natural numbers! You can create a bijection between these two sets. I can't see anything helpful about this example for kids, and in fact I think it teaches them the wrong intuition.

If you wanted to show different infinities, there might be a way to make Cantor's diagonal argument more accessible to children, to show them countable vs uncountable infinities, but that's a lot less intuitive!

What I mean by a bijection: in your example, you can map the nth dog to the nth paw, and each dog will always have a unique corresponding paw (albeit not its own paw, except for the first dog). Showing them different infinities would mean showing two sets where it's not possible to have this kind of mapping.

For example, an integer numbering to the set of all possible dog names (of unbounded length)