equivalently

equivalently, we can express this as a sum of squares.

equivalently, the problem can be viewed as an optimization task.

equivalently, consider the case where x equals zero.

equivalently, this statement is true regardless of the input.

equivalently, the two approaches yield the same result.

equivalently, let's define 'success' in a different way.

equivalently, the function is continuous and differentiable.

equivalently, we can rewrite the equation using logarithms.

equivalently, the two systems are mathematically consistent.

equivalently, this can be interpreted as a boundary condition.

equivalently, the algorithm converges to a stable solution.