I wondered a lot how to go on proving the applicability of two-element numbers in the probability theory. In my article titled "The mathematics of quantum theory I" I said that in the probability of the macro-world, two-element numbers can be used, or more precisely parabolic numbers can be used as probability amplitudes. This feasibility is foreshadowed by the property of the parabolic numbers: In their sum and multiplication the moduli of the second component of the parabolic numbers do not affect the moduli of the first component of the sum or of the product, and that the sum of the squared moduli of the probability amplitudes, i. e. the classic probability is nothing else than the square of the moduli of the first element of the parabolic number, so it does not depend on the moduli of the second element of the parabolic number. It would be interesting to consider how the probability theory with parabolic numbers would benefit instead of counting with real numbers in it. On this basis, it would be logical if first I considered the probability methods, formulas with the use of parabolic numbers, and I checked whether I can find a contradiction somewhere or whether I come to a conclusion counting with the parabolic numbers that it is verifiable by experience but does not arise from the classical probability theory with real numbers. For now, I do not follow this path, but I will think over the probabilistic model of quantum physics because we already use two-element numbers in it, and decades of experience has proven the usefulness of this mathematical method. In the quantum theory, the notion of probability amplitude and the classical notion of probability are separated, so I hope that a general probability model can be constructed more easily based on these.

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