Bound for Supremum of the Intersection of Sets | Real Analysis Exercises

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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.

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I had a problem with understanding real analysis, but I found things so simple with you. would you please make more videos explaining real analysis?

mrymfarhat

thank you so much, i really appreciate it, you make me love math, even though i'm an IT student :p

anonymousvevo

Shouldnt it be min( sup(A), sup(b)) i think this is wrong

thehardlife

go up more exercises are level exercises

samuelporras

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