Hi John Green;
I am afraid your conception of 16 year olds is not perfect.
I am 14 and I realise that f(n)=2n does a very good job of bijecting [0,1] to [0,2] which would pretty much imply the same cardinality.
I do not mean to say that there is no truth in your reasoning about kids. You are sort of correct about abstract reasoning but 16 is a little too old. 12 would be okay.
I'd have used the concepts of Aleph-Null and Aleph-One to explain my significant other on different sorts of infinities. Hilbert's hotel is even better.
By the way, do you think that there exists a set whose cadinality is strictly between that of natural numbers and reals.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.