401.1Y Proving the density of the rationals

[@manojvasan8111]

Really loved it When u say we assume the first step of the proof it is quite obvious from archimedis 😃(n>1/b-a ). Since a

[@erythsea]

You’re a wonderful teacher. So funny and informative!

[@Heyday0848]

it really helps me, thank you from Korea.

[@김명자-g8z]

Thank you from Korea, too !

[@boutiquemaths]

Love your style - thanks for this!

[@shyamdas6231]

If a and b are negative real numbers, how can we use Archimedean principle? In the video when p, p-1,p+1 etc is introduced, we are assuming a and b to be positive numbers.

[@farukgurbuzer2020]

actually no we’re not, we only assumed that b is greater then a which made b-a positive and that was enough for the proof. you can also see it by taking two negative irrational numbers.

[@bsteele1889]

Dude, you’re a really good professor

[@Ryan라이언]

Simple, concise and easy to understand

[@MelPeters7]

Since a-b ∈ R and also 1 ∈ R; (a-b)n > 1 or n > 1/(a-b)

[@vincentd1992]

Thanks for the clear explanation!

[@martinschmidt3046]

How did you justify that if p is the nearest integer to na +1 , p gonna be greater than na? I think that desearves a prove

[@Aliali-so4yh]

thanks you sir for your help full work ,,but i think if we make p element of Z not from N it well be clear ?

[@jinyuhu5432]

yes, it is. man, thanks

[@margaritakochurova7550]

Thank you for the video! However, my professor doesn’t let us use just pictures to proof something:(

[@MatthewSalomone]

Most don’t- which is why they write books instead of making videos :)

[@davidblack3620]

thanks, very help full

[@kparag01]

Sir, which software is this?

[@MatthewSalomone]

Check out doceri.com . I use it for all my KZbin videos.