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Homework for Math 3210 Spring 2010 Week 6 Instructor: Rémi Lodh Due Fri. 26th Feb. Guidelines for homework • Please do all problems. • Try to be as clear as possible in your answers. • Write the proofs in the same way as in the lectures. • Staple your homework sheets together. Failure to do so will result in a points penalty. Homework Problem List (from Taylor’s Foundations of Analysis) §3.1 : 2,4,7,8 §3.2 : In the proof of Theorem 3.2.1 we assumed that if we split an interval I into two intervals I1 and I2 (not necessarily disjoint), then a function f : I → R must satisfy supI f = supI1 f or supI f = supI2 f . Prove this. (Hint: reduce to proving that if A, B are subsets of R, then sup(A∪B) = max{sup(A), sup(B)}.) §3.2 : 1,2,4,5,6 http://www.math.utah.edu/~remi/teaching/3210Spr2010/3210Spr2010.html 1