inf(S) = -sup(-S)

inf(S) = -sup(-S)
In this video, I present a neat identity relating inf and sup. This means that, from now on, everything that we say for sup will hold for inf as well. Moreover, using this, we can prove the greatest lower bound property. Enjoy!
Check out my Real Numbers Playlist: • Real Numbers
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[@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...❤❤.

[@NotoriousSRG]

I love how enthusiastic he is :3

[@user-yu1nd6qx4l]

Thank u Dr Show! More hugs from South Korea

[@kimsongll]

한국인 !!!

[@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

[@---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.

[@tmlen845]

when you turn things around, things are turned around

[@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?

[@subhamyonzone4323]

Great work👍👍👍

[@xnylim1232]

very good video thanks so much

[@brylemorga3262]

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

[@roberttelarket4934]

Peyam you are Supremum.

[@drpeyam]

Awwwww

[@sumittete2804]

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

[@drpeyam]

1 and 0 probably

[@cuonghienthaosonbuitrung2841]

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

[@brylemorga3262]

So almost all comment gets heart?

[@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.