Error Analysis Math Example 2

Solution

1. 1
   Error: checking finitely many examples does not prove a universal statement. The student has verified the claim for $n \in \{2,3,4\}$ but not for all integers.
2. 2
   Counterexample: $n = 0$: $0^2 = 0 = n$, so $n^2 > n$ fails ($0 \not> 0$).
3. 3
   Another: $n = 1$: $1^2 = 1 = n$, again fails.
4. 4
   Correct claim: $n^2 > n$ for all $n > 1$ (or for $n < 0$, since $n^2 \ge 0 > n$ for negative $n$).