Bound for Supremum of the Intersection of Sets Real Analysis Exercises

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=R2WsyhE_FpQ

If A and B are two bounded and nonempty subsets of the real numbers, then what is the supremum of their intersection? What is sup(A intersect B)? We cannot say for sure in general, but we can place an upper bound on the supremum. If A and B are bounded nonempty subsets of the reals then we know they both have supremums by the completeness axiom. Similarly, their intersection must have a supremum. We'll prove that the supremum of A intersect B must be less than or equal to the maximum of supA and supB. This result will follow pretty easily from the definition of supremum being a least upper bound. • Definition of Supremum and Infimum: • Definition of Supremum and Infimum of... • Supremum of the Union of Sets: • Supremum of the Union of Sets | Real ... • ★DONATE★ • ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: / wrathofmathlessons • ◆ Donate on PayPal: https://www.paypal.me/wrathofmath • Thanks to Robert Rennie and Barbara Sharrock for their generous support on Patreon! • Thanks to Crayon Angel, my favorite musician in the world, who upon my request gave me permission to use his music in my math lessons: https://crayonangel.bandcamp.com/ • Follow Wrath of Math on... • ● Instagram: / wrathofmathedu • ● Facebook: / wrathofmath • ● Twitter: / wrathofmathedu • My Music Channel: / @emery3050

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