Infimum of a set

Infimum of a set
In this video, I define sup's little cousin, the infimum of a set. It is like a minimum, except that it always exists.
Supremum of a set: • Supremum of a set
Check out my Real Numbers Playlist: • Real Numbers

[@bigback9226]

I finally understand these proofs. Took me an entire month, but finally.

[@blackpenredpen]

Isn’t it

[@cuonghienthaosonbuitrung2841]

I want blackpenredpen to say "All right. Thanks for watching" for his video. Like what dr. peyam said in the beginning of video

[@CliffStamp]

I would think of that in terms of limits, but the set/element notation is very elegant.

[@CossZt6]

Such a shame there isn't a notation reading 'Simp' in maths

[@qschroed]

do we not need to use the supposition that m1 > 0 anywhere? I'm trying to understand why this proves anything special about 0 being the inf if we didn't even use that assumtion for the proof.

[@drpeyam]

Nothing special about m1 > 0

[@qschroed]

@@drpeyam Wouldn't that mean that you could choose any m in example 3 for the inf and it'd be alright? (except for m < 0 and m > 1)

[@cobalius]

Mhhh soup c:

[@AditYa-sv1nz]

👍

[@user-rl5ts1vg3s]

how can you show such N exist in example 3, that will be greater than 1/M?

[@drpeyam]

Also the Archimedean property: For any real number there is an integer that is greater than it. Here 1/m is a *fixed* real number, so you can find an integer that is greater than it.

[@Kdd160]

U are obsessed with math

[@liivan2281]

What is the 'm' in this? It seems not normal..

[@konradklekowicki2180]

someone plays mincraft?

[@dramwertz4833]

doesnt everybody? XD

[@cobalius]

Too much nowadays

[@drpeyam]

How so?

[@cobalius]

@@drpeyam uhm for me it's a mix of technology and hardcore mods. Eating becomes rough as mining the world, on the other hand and with enough playtime it becomes much more like creative mode