-(a-b) = b-a (Proof) [ILIEKMATHPHYSICS]

This video references "Intro to Real Analysis" by Bartle and Sherbert Fourth Edition. For more details related to the context of this video, see section 2.1.
The definition of subtraction of two real numbers is given in the book (after Theorem 2.1.3) to be a - b := a + (-b). (2), (3), and (6) each come from 2.1.1 Algebraic Properties of R. (4) and (5) are lemmas we have proven previously.
Thanks and enjoy the video!

[@wol2403]

give this man a field medal

[@lachenmann]

I love the way that you not only enunciate these proofs, but also explain all the facts you are basing the proof on. Your videos are a very valuable resource for understanding!

[@charlottebuckner2402]

very nice proof

[@katiekatten8968]

i think a cleaner proof would be using the fact that real numbers have a negative such that a + (-a) = 0. then, if you want to prove b - a = - (a - b), then you should prove a-b + b-a = 0. then, b - a is the negative of a - b

[@iliekmathphysics]

In my opinion, that is definitely more elegant ☝️

[@4see300]

very cool