The Organization Of Infimums & Supremums Of Sets & Subsets

Описание: In this video, I prove that if A is a subset of B, then the inf(b) is less than or equal to inf(a) which is less than or equal to sup(a) which is less than or equal to sup(b).

This problem can be found in Dr. Jirí Lebl's free open-access textbook: "Basic Analysis I: Introduction to Real Analysis, Volume I"
https://www.jirka.org/ra/

Any feedback on how these videos can be improved would be great. I will be constantly updating these videos to ensure that everything is accurate. Thank you all for being such a great community. All content is released under Creative Commons "No Rights Reserved", so please feel free to use this video however you want.

My name is Kody Amour, and I teach free undergraduate mathematics courses on YouTube. I'm currently developing three YouTube courses simultaneously: Discrete Math, Linear Algebra, Real Analysis, Topology, Number Theory and Complex Analysis. These courses correspond to playlists that I am constructing indefinitely.

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Credit to all of the authors of all of the resources below that greatly helped influence this video.

Free open-access online math textbooks (I only use textbooks from this resource, since everything is free for my students):
https://aimath.org/textbooks/approved...

A free in-depth tutorial for SageMath: https://doc.sagemath.org/html/en/tuto...

Learn LaTeX in 30 minutes: https://www.overleaf.com/learn/latex/...
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My favorite math-oriented YouTube channels (in no particular order):
Aleph 0:    / @aleph0  
The Bright Side of Mathematics:    / @brightsideofmaths  
Math Visualized:    / @mathvisualized355  
Insights into Mathematics:    / @njwildberger  
ScienceClic English:    / @scienceclicen  
Stand-up Maths:    / @standupmaths  
Zach Star:    / @zachstar  
Numberphile:    / @numberphile  
3Blue1Brown:    / @3blue1brown  
MIT OpenCourseWare:    / @mitocw  
Khan Academy:    / @khanacademy  
PBS Infinite Series:    / @pbsinfiniteseries  
Lex Fridman:    / lexfridman