I am currently studying Analysis 1.In that they proved that the square root of 2 is an irrational number using the approximation of supremum concept and I'm floored.The proof itself makes use of 2 concepts (the completeness axiom and the law of trichotomy).I'm just in love with that proof right now.
Above are some pages from my journal.
Hope you are having a goody goody day 🍰