A Paradox in Rounding Errors Approximate Computing for Big Data

The primary goal is to introduce a new methodology into approximate computing for big numerical data. First, an unpleasant phenomenon in large scaled numerical computing is observed: The probability of getting "correct approximations" is near zero for big numerical data. Second, a theorem that echoes this observation is proved: Perfect approximations are impossible in classical approach (Theorem 1). Using Codd´s terms in relational databases, "time-varying" intervals are used to build the real number system (Theorem 2). If the effective computing procedure defines a continuous real-valued function P, then the P(approximate value) and P(true value) can be smaller than any given e. In other words, in this new approach, we find a perfect approximation (Theorem 3).