Lovely lay explanation of what it means for a number to be transcendental.https://twitter.com/danluu/status/1147983323483922433 …
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I can't resist mentioning a proof e is irrational. Suppose for a contradiction that it's not. Then e = 1 + 1/2! + 1/3! + ... = p / q for positive integers p & q. Multiply both side by q! & you see 1/(q+1) + 1/(q+1)(q+2)+... is an integer. But it's easily shown to be > 0 & < 1 QED
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Of course, the linked explanation of transcendental numbers, while clear, isn't very motivated. It'd be nice to have a good lay starting question - meaning, one that isn't just clear, but which seems interesting to a layperson - whose answer is "the transcendental numbers".
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Same idea, but more technical for pi...
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I don't know of a similar proof for pi. What's the proof using the same idea?
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