>>9256674>"There's no Diagonal set" because by hypothesis there is no subset of N that isn't enumerated by f(n) and the diagonal set is a subset of N.
This conclusion doesn't make any sense to me, the hypothesis that P is enumerable doesn't tell you anything about which naturals don't get sent to subsets containing them. Can you add more steps to explain how you come to this conclusion?
The argument is just:
Assume you have enumeration f
Consider the set D (you don't make any assumptions about D)
Since f was an enumeration there is some d mapping to D, so f(d)=D
If d is in D, then d is not in f(d)=D (by definition of D), a contradiction.
If d is not in D, then d is in f(d)=D (by definition of D), a contradiction.
Those are the only two possible cases, so the only assumption that was made must be false, i.e. P is not enumerable