My personal favorite relation between π and e 
Is there any other mathematician whose work is instantly recognizable?pic.twitter.com/WMliDN17Vs
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The square root of two plus its negative is zero, so the sum of two irrational numbers can be rational. Of course that’s a somewhat silly counterexample; if you add two “random” irrational numbers, their sum “should” be irrational. But Ramanujan’s two summands aren’t very random.
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I’m not sure what you mean. Complex numbers can be represented uniquely as the sum of a real part and an imaginary part, but there’s no comparable way to write a real number as the sum of a rational part and an irrational part. (But see http://mathworld.wolfram.com/HamelBasis.html .)
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That’s true.. I’m just imagining something like a+pi where a is rational.. I don’t think something like that could be written as the ratio of two integers
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