How do you prove that fractions are countablely infinite?
You can find the answer in this book for children. I read to my boy when he was around 6 or 7 years old. He was intrigued. Math is not difficult, it's just abstract. So the problem is that there is a dearth of good math teachers. Most people are floored by algreba, which is the key to higher level math learning.
The concept of Hotel Infinity was pioneered by David Hilbert, an eminent mathematican, though George Cantor was the mathematican who came up with the concept. So I suppose mathematicans at the pinnacle are not teaching children or teenagers. They are more interested in research.
Fret not, for there are still wonderful books like The Cat in Numberland around :)
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