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I was surprised when I learned that e + pi is not known to be transcendental. Everyone would be floored if it weren't, but it's still an open question.
by tgb 8y ago
I was surprised when I learned that e + pi is not known to be transcendental. Everyone would be floored if it weren't, but it's still an open question.
- pbhjpbhj 8y agoSeems like there should be an easy proof of that ...
- tzs 8y agoIt's not even known if e + pi is irrational. It is known that at least one of e + pi and e pi is irrational, though. That's because e and pi are both transcendental, and so the polynomial (x-pi)(x-e) = x^2 - (e+pi)x + e pi cannot have all rational coefficients. If it did, e and pi would be roots of a polynomial with rational coefficients, and therefore not transcendental.