Squaring Both Sides Of An Inequality (With Proof Using The Axioms Of Ordered Fields)
In this video, I prove that if 0 is less than x and x is less than y, then x^2 is less than y^2 (where x and y are elements of an ordered field F).
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