[Ferrotin]

I remember being a kid and having this discussion in elementary school. Kids have enough intuition to know that operations with fractions should get the same result as with decimal numbers. Or that 1-0.999… = 0.000…. Or that different lengths have a length in between them. All are legitimate and compelling arguments.

[amelius]

I think lots of students get lost with different orders of infinity (countable, uncountable, etc.), so I think there is definitely a point beyond which you can't push the intuition behind infinite objects.

[naasking]

> Or that different lengths have a length in between them. All are legitimate and compelling arguments.

Except that's wrong, not all lengths do have a length between them.