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A joke in approximating numbers raised to irrational powers

(www.andreinc.net)
104 points nomemory | 1 comments | 18 Nov 24 16:41 UTC | HN request time: 0.208s | source
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enugu ◴[19 Nov 24 19:04 UTC] No.42186957[source]▶
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_theo...

replies(2): >>42187274 #>>42187305 #
wging ◴[19 Nov 24 19:41 UTC] No.42187305[source]▶
Small 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.
replies(1): >>42191189 #
1. enugu ◴[20 Nov 24 06:04 UTC] No.42191189[source]▶
Yes, I should have mentioned polynomials with rational coefficients(or indeed any algebraic numbers as coefficients due to transitivity of being algebraic).