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Can you produce a rational number by exchanging infinitely many digits of pi and e?

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Hierarchy of Infinities
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Links to other resources:

Original Post from Math Overflow
http://mathoverflow.net/questions/265...

Square Root of 2 is Irrational
http://www.mathsisfun.com/numbers/squ...

Written and Hosted by Kelsey HoustonEdwards
Produced by Rusty Ward
Graphics by Ray Lux
Made by Kornhaber Brown (www.kornhaberbrown.com)

Thanks to Joel David Hampkins and Erin Carmody for helpful comments.

Comments answered by Kelsey:

Circuitrinos
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​Brian Willett​
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