2 ms·
One interesting result implies that numbers like 3^(sqrt(3)) will be transcendental (ie no polynomial will evaluate them to 0). https://en.wikipedia.org/wiki/G
by enugu 2y ago
One interesting result implies that numbers like 3^(sqrt(3)) will be transcendental (ie no polynomial will evaluate them to 0).
https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theorem https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_theo...
- immibis 2y agoNo polynomial with rational coefficients. Of course x-y evaluates to 0 when x=y, even if y is a transcendental number.
- wging 2y agoSmall but important correction: no polynomial with integer coefficients (equivalently, rational coefficients). p(x) = (x - 3^(sqrt(3))) is a perfectly fine polynomial with real coefficients.
- enugu 2y agoYes, I should have mentioned polynomials with rational coefficients(or indeed any algebraic numbers as coefficients due to transitivity of being algebraic).