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Astounding!

What are the most astounding mathematical facts accessible to school pupils? We're looking for a Top Ten here and to make a start, here are some offerings from MathsNet:

eip+ 1=0

1=0.999...

00=0 or 1. Which one and why?

Fractals


From Gabriel Solari: There are infinitely many real numbers between 0 and 1.


Inspired by an article in MT 161, Mathematics Teaching, December 1997.
What do you think the most astounding mathematical fact is?
Let us know.

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