Hi, I'm self studying analysis, and I'm having problem with this proof. I've gotten most in my book so far but this has posed a problem.

I've attached the problem.

for part 1 I just said A is non empty since when x = 1/5 and n = 5 1 is an integer

for part 2 I let k = 1, x = 3/2 and showed that 1 < 3/2 < 2

For part 3 and 4 I have no idea what to do and i'm not sure whether i've done the prior correctly. I'd appreciate any help. Thanks!