Proof that Closed Balls are Closed Sets Part 1

[@Naruto16081992]

Hey where is the previous video? i watched the previous video in the playlist where it is proven that all open balls are open sets.This video starts from middle of a something i guess.could you please let me know the video prior to this?

[@gerald_the_science_guy]

U sir, are single handedly coasting me through topology. omgTHANK YOU!!!!

[@tekaaable]

same here :)

[@yantinglee4803]

Hi is there another video before this showing clopen sets?

[@yusufdadkhah7561]

you can think about the proof like this as well here is our number set ρ=|x−y|ϕ=R−R R=R−ϕ the logic behind why all of these number sets are not open and not closed is if you have R and ϕ in our number set, it stops all the numbers sets being open and closed and since we had R and ϕ in our number set ,the number set was not open and closed because of that rule

[@snowy3653]

Everything will be cool but be careful guys. There should be all the time h - r, not r - h because r - h < 0 and then it doesn't make sense. We have our first triangle inequality, that's cool, and then we add by both sides d(x,z)

[@anthonyhashemi8808]

you're a g, cheers chap

[@joseluisarmenta-lm4we]

if y =0 is not a rect is not a funciton and is not zero set sir