![SOLVED: EX.s: Prove the following facts about sup and inf. (All the proofs should follow directly from the definition: The statements are fairly intuitive and You may find it helpful to draw SOLVED: EX.s: Prove the following facts about sup and inf. (All the proofs should follow directly from the definition: The statements are fairly intuitive and You may find it helpful to draw](https://cdn.numerade.com/ask_images/9c78459c31cf4313ba99ead636ab8364.jpg)
SOLVED: EX.s: Prove the following facts about sup and inf. (All the proofs should follow directly from the definition: The statements are fairly intuitive and You may find it helpful to draw
![SOLVED: Question %: For two sets A, B define A + B = a +bla € A,b e B Prove Or disprove that inf(A + B) = inf A + inf B SOLVED: Question %: For two sets A, B define A + B = a +bla € A,b e B Prove Or disprove that inf(A + B) = inf A + inf B](https://cdn.numerade.com/ask_images/47da112420294df48d97cd0c05bcb563.jpg)
SOLVED: Question %: For two sets A, B define A + B = a +bla € A,b e B Prove Or disprove that inf(A + B) = inf A + inf B
![SOLVED: Suppose Ihat A and B are bounded subsets of R Prove that UB is bounded and that sup(A U B) sup sup A, sup B For A, B, subsets of R, SOLVED: Suppose Ihat A and B are bounded subsets of R Prove that UB is bounded and that sup(A U B) sup sup A, sup B For A, B, subsets of R,](https://cdn.numerade.com/ask_images/cf4681a8eba24a48b2bceed07d8b65a1.jpg)
SOLVED: Suppose Ihat A and B are bounded subsets of R Prove that UB is bounded and that sup(A U B) sup sup A, sup B For A, B, subsets of R,
![Sup (A+B) = Sup A + Sup B | Properties of Supremum and Infimum | Real Analysis | Lease upper bound - YouTube Sup (A+B) = Sup A + Sup B | Properties of Supremum and Infimum | Real Analysis | Lease upper bound - YouTube](https://i.ytimg.com/vi/ZZALH8HOSXk/maxresdefault.jpg)
Sup (A+B) = Sup A + Sup B | Properties of Supremum and Infimum | Real Analysis | Lease upper bound - YouTube
![SOLVED: 14. For A, B; subsets of R, define A + B = a + b:aeA,be B and A . B = ab : a e4,b e B: 4. For A = - SOLVED: 14. For A, B; subsets of R, define A + B = a + b:aeA,be B and A . B = ab : a e4,b e B: 4. For A = -](https://cdn.numerade.com/ask_images/01f593d21a7d4bc0bb6b77c68218b652.jpg)
SOLVED: 14. For A, B; subsets of R, define A + B = a + b:aeA,be B and A . B = ab : a e4,b e B: 4. For A = -
![SOLVED: Show that if A and B are bounded subsets of R, then AU B is bounded set, and 1) sup(AU B) maxsup A,sup B, 2) inf(AU B) = mininf A,inf B. SOLVED: Show that if A and B are bounded subsets of R, then AU B is bounded set, and 1) sup(AU B) maxsup A,sup B, 2) inf(AU B) = mininf A,inf B.](https://cdn.numerade.com/ask_images/21dfd80bc11241b99496c2d0cdd5269d.jpg)
SOLVED: Show that if A and B are bounded subsets of R, then AU B is bounded set, and 1) sup(AU B) maxsup A,sup B, 2) inf(AU B) = mininf A,inf B.
![sup(A+B)=sup(A)+sup(B), inf(A+B)=inf(A)+inf(B), A, B are non empty bouded subsets of R, Rudin,Lec 19 - YouTube sup(A+B)=sup(A)+sup(B), inf(A+B)=inf(A)+inf(B), A, B are non empty bouded subsets of R, Rudin,Lec 19 - YouTube](https://i.ytimg.com/vi/sJnSnVXX6Ic/sddefault.jpg)
sup(A+B)=sup(A)+sup(B), inf(A+B)=inf(A)+inf(B), A, B are non empty bouded subsets of R, Rudin,Lec 19 - YouTube
![SOLVED: Let A, B € R be non-empty sets. We define AB = ab a € A,b e B- Assume that both A, B are bounded and subsets of [0, ) = SOLVED: Let A, B € R be non-empty sets. We define AB = ab a € A,b e B- Assume that both A, B are bounded and subsets of [0, ) =](https://cdn.numerade.com/ask_images/174d1a6f75c84d26b388fbf3e59ee464.jpg)