Odd Equations - Numberphile
Second part to this video: http://youtu.be/shEk8sz1oOw
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: http://youtu.be/JmyLeESQWGw
Dedekind cuts: http://en.wikipedia.org/wiki/Dedekind_cut
Support us on Patreon: http://www.patreon.com/numberphile
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Видео Odd Equations - Numberphile канала Numberphile
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: http://youtu.be/JmyLeESQWGw
Dedekind cuts: http://en.wikipedia.org/wiki/Dedekind_cut
Support us on Patreon: http://www.patreon.com/numberphile
NUMBERPHILE
Website: http://www.numberphile.com/
Numberphile on Facebook: http://www.facebook.com/numberphile
Numberphile tweets: https://twitter.com/numberphile
Subscribe: http://bit.ly/Numberphile_Sub
Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile
Videos by Brady Haran
Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/
Brady's latest videos across all channels: http://www.bradyharanblog.com/
Sign up for (occasional) emails: http://eepurl.com/YdjL9
Numberphile T-Shirts: https://teespring.com/stores/numberphile
Other merchandise: https://store.dftba.com/collections/numberphile
Видео Odd Equations - Numberphile канала Numberphile
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