Convex Sets | Introduction, Definition and Examples

[@Gibson-xn8xk]

When i see the material represented in a such cool way, i feel a need to write a comment. Thank you for the time and the work you have done.

[@aviralsood8141]

These videos are incredible! Great work.

[@DrWillWood]

Thanks a lot!

[@BRYDN_NATHAN]

Thank you. 0:05:01 👍

[@MrCliverlong]

Very clear explanation with clear graphics. Thanks

[@hadidwindoro]

This is very helpful! thank you!

[@Mothuzad]

Nice video! When I thought through this at the beginning, I imagined that the convexity would rely on a definition of a mean for the given set. However, when I saw you give the linear interpolation definition, I thought a little more and realized that my idea would allow fractals which aren't convex, such as the set of all numbers n/(2^k) where n and k are non-negative integers. It would include every whole number and yet it would miss infinitely many rationals (such as 1/3), despite clearly including the midpoint of any two elements.

[@amritawasthi7030]

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[@DrWillWood]

thanks a lot! :-)

[@Imaginary_Paul]

@Dr. Will Wood, at time 3:40 the example you have shown will also satisfy for Rhombus(with respect to one norm prospect)

[@2false637]

This series is superb. Keep it up!

[@DrWillWood]

Thanks so much! I will do!

[@bernardofitzpatrick5403]

Hope you will be posting more vids🤙🏽 . subscribed

[@DrWillWood]

Thanks a lot! definitely will be :-)

[@CricMania000]

this is awesome

[@elijahgemmill2000]

Giving my university lecturers a run for their money.

[@HeavenlyGodlyAngelic]

Thank you

[@minari3274]

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[@llllllllllllllll777]

Thank you a lot❤

[@8685mike]

This is great! Is there an example of a concave set? What set of functions won't work the way polynomials of degree 2 did?

[@abhinavkumarverma1017]

I think we need to ensure A is not zero else the C will become a polynomial of degree 1 or less. Maybe you have to say set of polynomials of degree 2 or less is convex.

[@arindambasu4616]

Nice video. Surprised why view is so less.

[@zorm_]

the set of polynoms of degree d=2 is not convex the set of polynoms of degree d

[@MirtaTroyer]

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[@matematicaspanish8301]

What if you have two quadratic polynomials with main coeficients 1 and -1? there will be a polyinomial middway that loses one degree. Shouldn't we consider the set of polynomials of degree less or equal than 2 as the convex one?

[@DrWillWood]

Hi, yes sorry I wasn't clear there! generally I consider "the set of nth order polynomials" to be those including those with zero as the coefficient of x^n. I'm not sure whether this is a common definition but it works well in this kind of situation!