Math Investigation eTwinning. Mission: Infinity...Affairs! Volume: Infinity | Page 12

Now we follow a path through this square, and every time we see a valid rational number, we pair it
up with the next integer: once again, we can be sure not to forget any rational number.
And this is really quite surprising: remember that there are infinitely many rational numbers
between 0 and 1. (Actually, there are infinitely many rationals between any two distinct numbers,
no matter how close they are.) But since we can pair up all these rationals with the natural numbers,
there must be the same number. Infinity times infinity is still infinity.

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LYKEIO SCHIMATARIOY, GREECE

- VALLAURI FOSSANO, ITALY

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