1. The problem asks us to prove that $1=1$. 2. This is an identity, meaning it is true by definition. 3. The number $1$ is the multiplicative identity in the number system, meaning for any number $a$, $a \times 1 = a$. 4. Since both sides are identical and defined the same, $1$ equals $1$ trivially. 5. Therefore, the proof is complete: $1=1$ is true by definition.