The way I would explain it to a 6 year old would be like this:
There are natural numbers, like 0,1,2 and so on. Natural numbers can be odd or even. There is no such natural number as infinity. Therefore the question if 'infinity' is odd or even is meaningless. It does not even type-check.
In math people like well-formed questions, and generally don't like ill-formed questions.
The fallback metaphor I use in these situations or similar ones, "What's outside of the universe" for example, is the old, "What's North of the North Pole?" Then you explain that we can create questions and statements in our languages which don't have logical, mathematical or physical validity. Although we can often describe scientific and technical concepts in common languages, that's just a translation, the real language is math.
Carlos Castaneda is at his most interesting when he wrestles with "what's outside of the universe" paradoxes since his informants seem like they're able to not only hold mutually exclusive concepts but exist in a relationship between them. They'd have an internally consistent idea about what's North of the North Pole and could explain it to you in terms you might understand.
He's given me quite a bit to think about in regard to NULL and the assumptions I make around the concept, which is fascinating in itself because his books are hot garbage.
The first one is basically "Fear and Loathing on the Campaign Trail '72" for anthro majors, and then he gets less focused somehow. He'd be my personal Kilgore Trout if we didn't have contemporary science fiction.
> In math people like well-formed questions, and generally don't like ill-formed questions.
This is not so simple, though. Ill formed questions can be interesting as a motivation to formalise them (ie make them well-formed) in generalising/abstracting concepts into new concepts. Eg how even/odd has been generalised to transfinite numbers.
If you try hard enough, you can find similar questions, that do type-check. You can talk with 6yo children about them if you want. Still, I stand with my answer. I would say this (also I think this is the best thing to say/I am capable of).
There are natural numbers, like 0,1,2 and so on. Natural numbers can be odd or even. There is no such natural number as infinity. Therefore the question if 'infinity' is odd or even is meaningless. It does not even type-check.
In math people like well-formed questions, and generally don't like ill-formed questions.