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.
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