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Second part to this video: More links & stuff in full description below ↓↓↓ If the highest power of a function or polynomial is odd (e.g.: x^3 or x^5 or x^4371) then it definitely has a solution (or root) among the real numbers. Here's a nice proof demonstrated by Prof David Eisenbud from the Mathematical Sciences Research Institute. At 10:33 Prof Eisenbud intended to say “no rational roots“ rather than “no real roots“. At 2:52 we should have put (2,5) rather than (2,4). Also, Prof Eisenbud adds that “The Dedekind cut corresponding to the root is: (Rationals x where f(x) is less than or equal to zero) (Rationals x where f(x) is greater than zero)“ Numberline stuff: Dedekind cuts: Support us on Patreon: NUMBERPHILE Website: Numberphile on Facebook: Numberphile tweets: Subscribe: Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): Videos by Brady Haran Brady's videos subreddit: Brady's latest videos across all channels: Sign up for (occasional) emails: Numberphile T-Shirts: Other merchandise:
