numberphile sum of natural numbers 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...

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/n...

numberphile sum of natural numbers Odd Equations - Numberphile
11,163 Likes	11,163 Dislikes
870,689 views views	3.05M followers
Science & Technology	Upload TimePublished on 10 Jun 2014

Related keywords

maths is fun,solution explorer,solution center,roots significado,numbers in japanese,roots cafe,polynomial calculator,equation for work,roots lyrics,numberphile 1+2+3,equation balancer,polynomial division,roots traductor,rootstock,roots bloody roots lyrics,numberphile 1+2+3+4,numbers of pi,equation of a circle,numberphile good will hunting,numberphile golden ratio,solution essay,solution center özyeğin,equation simplifier,numbers to letters,roots traduccion,math solver,solution ne demek,polynomial regression machine learning,mathsframe,mathematics mos def,maths meme,roots bloody roots,mathspace,mathseed fremont,numbers in korean,numberphile podcast,polynomial equation,polynomials exercises,mathematics definition,mathscinet,mathscore,polynomial fit python,equation solver,mathematics in spanish,numbers in french,maths online,numberphile pi,mathematics major,polynomial division calculator,numberphile wiki,numbers on a check,numberphile james grime,polynomial interpolation,mathematics science and technology,numbers in chinese,mathematics degree jobs,maths olympiad,polynomial definition,equation of a line,equation for velocity,mathematics of poker,maths games,numbers in german,polynomial regression matlab,solution architect,numberphile 1/12,polynomial roots calculator,numbers to prank call,solution explorer visual studio,numberphile meaning,equation of a parabola,equation editor,mathematics of finance,equation for power,mathematics wu tang,roots canada,mathematics vision project,maths questions,roots imagine dragons,solution oriented,polynomial regression python,polynomial regression,mathematics museum,roots movie,maths puzzles,numbers 5,polynomial regression sklearn,equation definition,rootstack,numbers cast,mathematics degree,numberphile card trick,equations of motion,equation calculator,numberphile reddit,mathematics for economists,numbers 18 21,solutions promena,solutions krem ne işe yarar,polynomial long division,solution provider,equation of hyperbola,roots serie,solution synonym,numbers in italian,polynomial function,solution nedir,solutions,equation of an ellipse,mathematics for computer science,roots hostel,solution partner,solution pack,mathematics for machine learning,roots reggae,polynomialfeatures,numbers in english,numberphile youtube,mathematics that works for geometry answers,solutions ne demek,numberphile klein bottle,mathematics jobs,numberphile merch,roots en español,maths problem solving,equation for cellular respiration,equation for acceleration,mathway,roots matlab,mathematics books,numbers ny,mathsnacks,numberphile greentext,polynomial kernel,polynomial regression in r,equation for photosynthesis,mathseeds,solutions türkiye a2,solutions türkiye a1,roots sepultura,mathematics lyrics,numbers in spanish,maths genie,numbers to words,roots rock reggae,polynomial factorization,numbers tv show,mathshell,equation for volume,mathematics genealogy,equation of a plane,numberphile 301,numberphile 意味,numbers in arabic,roots letra,solution inn,numberphile circles,numbers to call,mathswatch,