And that is why you don't miss maths classes in college/university unless your city has
been nuked or you're completely dead...honest!
1) We get that for or any
It's easy to see that in both cases we get that the resulting fraction is greater than or
equal 0.5, so choosing , say, and calling the sequence , we get that for any
n, , which contradicts the definition of Cauchy seq. (just take m = n+1)
2) For such a sequence, if we have different elements, then , but as the
seq. is Cauchy take say ...and end
now the argument.