Assignment # 01 MTH621 (Spring 2020)

Maximum Marks: 20 Due Date: 10 -06-2020

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Q1. Let S and T be nonempty sets of real numbers and define

S-T={s-t│s∈S,t∈T}.

Show that if S and T are bounded, then

sup(S-T)=supS-infT

and

inf(S-T)=infS-supT

Q2. For what integer n is

1/n!>8^n/(2n)!?

Prove your answer by induction.