Open, closed, both and neither sets

This video briefly explores (in R) sets that are open, closed, neither and both (clopen)

[chemdah]

Thanks for this. Word of the day, 'Clopen'.

[princeatsrim]

THANK YOU, THIS REALLY HELPED ME UNDERSTAND THE TOPIC. I WISHED YOU POLISHED THE VIDEO WITH SOME FEW EXAMPLES

[erinmeyers-tw]

thank you... helping maths students for generations to come

[raydencreed]

You seem to be very responsive in the comments here, so I’ll go ahead and ask... well, I guess a few questions.

First of all, thanks for the video. It helps a ton.

1. Would it be the case that for like a two-dimensional blob in R^2, a non-open, non-closed set would be where that blob has a section of its boundary dotted and a section of its boundary completely filled in? Similar to how for the non-open, non-closed set in your video has part of the boundary not included and part included? Or am I misunderstanding what makes it non-open and non-closed?

2. Does it always have to be the case that a clopen set has to be infinitely extending in some directions. Like, could the only clopen set in R^2 be the whole plane?

[kyometzu]

Right now I'm in 6th grade but I am in the top .01% percent of mathematicians my age. I have a question though right now I'm in topology and one of my questions states. For each of the following, use the green- red convention to draw a figure in a plane pi, and then argue whether it is open in pi, closed in pi, or both. How would you draw this for a line PQ - the roster name P, Where P, Q are distinct points in pi.

[gamer]

i want to complain about the audio... but this helped me

[AG-]

how every single point in R set is a limit point? as limit points are -infinity & +infinity

[dixonyamada]

why does R contain all of its limit points, that is, why is R closed? if you have a limit point in R, call it x, then the next point (x + 1) cannot also be a limit point as it is a value that exceeds the limit point x, meaning that if a point exceeding x really exists, then x cannot be a limit point (it can still be a point hit by the ball but not THE limit point), and that new point (x + 1) must be the actual limit point. but since R goes from negative infinity to infinity, there must be x+2, x+3, and so on, so from what I know the limit point is ambiguous. I know 1000% this is wrong but prove to me why cos i cant wrap this 'clopen' thing in my head.

[JasonDangol]

Thank you very much for the video! Btw, (1, 4) ⋂ (3, 5) should be closed right, since intersection is [3, 4] ?

[matteoteo]

the set of natural number N is close or open?

[megp]

What happens if you have a union of open closed sets? eg. [0, 1)U(1, 2] ?

[tensorfeld]

The sound: wruummmm! XD

But good explanation!

[ذوالفقار-رن]

Sir i am not understanding well what is the relation of absimum in the issue and what the realtion of number 1 also in this lesson if less than 1 bigger and of the inclusion and complement i am gone in this

[paradoxjihoon]

if a set has only one element, is it closed?

[shrimatkapoor]

Wtf is that creepy ass music at the start