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Some classics are Zeno's paradoxes (infinity, limits) and Hilbert's Infinity Hotel. Let's make up more!

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**Answer** by Denise Gaskins
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Aug 15, 2013 at 02:26 PM

My now-teen daughter still remembers the "infinite cake" activity (cutting a square into ever-smaller pieces) we did a couple years ago. She's used it in geometry proofs a couple of times this year.
The 1/2's version is certainly accessible to 5-year-olds, and probably the 1/3's version as well. Beyond that, the fractions might get tricky, although the basic idea that the limit is 1/(n-1) is easy to explain: We all split a cake evenly, but then Mom (who is on a diet) decided she didn't need her whole piece. So we split her piece between everyone. But then Mom decided that even that piece-of-a-piece was a bit more than she needed, so we split her part again, and again... In the end, how many people shared the cake?

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