equivalently, therefore
equivalently, therefore
equivalently stated
equivalently stated
equivalently expressed
equivalently expressed
equivalently defined
equivalently defined
equivalently described
equivalently described
equivalently, it follows
equivalently, it follows
equivalently, consider
equivalently, consider
equivalently, namely
equivalently, namely
equivalently, thus
equivalently, thus
equivalently speaking
equivalently speaking
equivalently, we can express this as a sum of squares.
equivalently, we can express this as a sum of squares.
equivalently, the problem can be viewed as an optimization task.
equivalently, the problem can be viewed as an optimization task.
equivalently, consider the case where x equals zero.
equivalently, consider the case where x equals zero.
equivalently, this statement is true regardless of the input.
equivalently, this statement is true regardless of the input.
equivalently, the two approaches yield the same result.
equivalently, the two approaches yield the same result.
equivalently, let's define 'success' in a different way.
equivalently, let's define 'success' in a different way.
equivalently, the function is continuous and differentiable.
equivalently, the function is continuous and differentiable.
equivalently, we can rewrite the equation using logarithms.
equivalently, we can rewrite the equation using logarithms.
equivalently, the two systems are mathematically consistent.
equivalently, the two systems are mathematically consistent.
equivalently, this can be interpreted as a boundary condition.
equivalently, this can be interpreted as a boundary condition.
equivalently, the algorithm converges to a stable solution.
equivalently, the algorithm converges to a stable solution.
equivalently, therefore
equivalently, therefore
equivalently stated
equivalently stated
equivalently expressed
equivalently expressed
equivalently defined
equivalently defined
equivalently described
equivalently described
equivalently, it follows
equivalently, it follows
equivalently, consider
equivalently, consider
equivalently, namely
equivalently, namely
equivalently, thus
equivalently, thus
equivalently speaking
equivalently speaking
equivalently, we can express this as a sum of squares.
equivalently, we can express this as a sum of squares.
equivalently, the problem can be viewed as an optimization task.
equivalently, the problem can be viewed as an optimization task.
equivalently, consider the case where x equals zero.
equivalently, consider the case where x equals zero.
equivalently, this statement is true regardless of the input.
equivalently, this statement is true regardless of the input.
equivalently, the two approaches yield the same result.
equivalently, the two approaches yield the same result.
equivalently, let's define 'success' in a different way.
equivalently, let's define 'success' in a different way.
equivalently, the function is continuous and differentiable.
equivalently, the function is continuous and differentiable.
equivalently, we can rewrite the equation using logarithms.
equivalently, we can rewrite the equation using logarithms.
equivalently, the two systems are mathematically consistent.
equivalently, the two systems are mathematically consistent.
equivalently, this can be interpreted as a boundary condition.
equivalently, this can be interpreted as a boundary condition.
equivalently, the algorithm converges to a stable solution.
equivalently, the algorithm converges to a stable solution.
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