The next lesson for the Naturals was a lesson about numbers and sets. It was given by Professor Cantor in his office. He was a proud-looking man with a receding hairline, neat beard, and big nose. He paced up and down with his hands behind his back and explained:
“There are many notations for the numbers in mathematics. You will all be familiar with the Roman system, which denotes 'one' with a single vertical stroke, 'two' with two strokes, and 'three' with three. It gets more complicated after that, of course, which is one of the reasons it isn't used so much any more. Arabic numerals are more economical – there's a single symbol for all the numbers up to 10 – but it's not intuitive like the Roman system, so how can you remember which symbol is which?” He proceeded to answer his own question. “The key is in the number of angles. One has only one angle, two has two, three has three, and so on.”
'Nice one,' reflected Paidia, 'but it only goes so far. How would he explain 6 and 9 which are the same as each other but just the other way up? It's neat, but rather far-fetched.'
Professor Cantor took a few more turns in front of the