inf(S) = -sup(-S)

[@NotoriousSRG]

I love how enthusiastic he is :3

[@leonardosaads]

I loved the video. Could you then make more topology-related videos? Hugs from Brazil! (Abraços do Brasil)

[@drpeyam]

Check out my metric spaces playlist (somewhere on my channel), it has lots of topology

[@drpeyam]

kzbin.info/aero/PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI

[@Navjot0704]

Love from India...❤❤.

[@듈이-k2b]

Thank u Dr Show! More hugs from South Korea

[@kimsongll]

한국인 !!!

[@---nw8qu]

I am definitely the worst student in the class.

[@drpeyam]

You can’t be, the worst students don’t even watch the videos 😉

[@---nw8qu]

@@drpeyam I saw the Numberphile video from today about the trigonometric functions. It was very interesting because I never saw the trig functions taught in that way.

[@luisibalaz]

This was a question on my Calculus 1 exam. I nailed this haha.

[@drpeyam]

Wow, what a Calc 1 class! Haha

[@luisibalaz]

@@drpeyam yeah, it was pretty wild

[@MuniraDanish-w9x]

Thank you so much that was very clear

[@drpeyam]

Glad it was helpful!

[@jimmykornelijegunnarsson4265]

Question about the proof at 9:00, Suppose we instead define some set S such that all elements of S is defined as {s_k}k_0->inf: s_0 = m, s_inf = M. Wouldn't that be sufficient given it's a closed interval?

[@tmlen845]

when you turn things around, things are turned around

[@subhamyonzone4323]

Great work👍👍👍

[@brylemorga3262]

Inf sup: sup sup sup sup sup ................

[@xnylim1232]

very good video thanks so much

[@sumittete2804]

Sir ...what are the supremum and infimum of (0,1) intersection {m+n√2 : m,n are integers}?

[@drpeyam]

1 and 0 probably

[@roberttelarket4934]

Peyam you are Supremum.

[@drpeyam]

Awwwww

[@brylemorga3262]

So almost all comment gets heart?

[@cuonghienthaosonbuitrung2841]

very very very very ... (infinity many times) cool

[@kimsongll]

SUS

[@eliyasne9695]

How come all your hypothetical students are mediocre? (You are not the best student in the class, there's someone better than you... You are not the worst student in the class, there's someone worse than you...)

[@drpeyam]

Hahahaha

[@iabervon]

His class is an open interval, so nobody in his class is either the best or worst student in it. Kind of a weird class, but that's analysis for you.