Determine intS and explain why n 1 1n SolutionLet c0 So by A

Determine int(S) and explain why.

Solution

Let, c>0 So by Archimedean property there exists n so that

nc>1 or c>1/n

Hence c does not belong to the set: (-1,1/n)

Hence c does nto belong to S

Now, -1<0<1/n for any n so 0 belongs to S

Hence, S=(-1,0]

int(S)=(-1,0)