Fill in the blanks in the following proof. Claim: Let xn = 1 + for all n E N. Then x,, does not converge to zero. n NEN we take n = Proof: Take € = | 1 + //| = 1 + //| ≥ € n which completes the proof. N+1 Then 1 for all 2 N-1 Then n we choose 0 N and we verify:

Can you show me how to solve this?

Choose the answer that best completes the proof that inf(A)=0 where A = Firstly, we would show that o is a lower bound for A by noticing that 0s for all nEN- n2 Then.. O None of these O Then we would let W>0 be arbitrary but fixed and show that W can't be a lower bound for A: 1 0 it follows, from the Archimedean Property, that there exists NEN such that O Then we would let W>0 be arbitrary but fixed and show that W can't be a lower bound for A: Since W>0 it follows that we can choose EA such that " 0 be arbitrary but fixed and show that W can't be a lower bound for A: Since W>0 it follows, from the Archimedean Property, that there exists NEN such that