Abstract
The advantages and disadvantages of the procedure of fixing the values of fundamental physical constants (FPC) for redefining the basic SI units are examined. The case in which a fixed value of the Avogadro constant is used simultaneously for new definitions of the unit of mass and the unit of the amount of matter is discussed in detail. A criterion is proposed for choosing the optimum set of FPC with fixed values for redefining basic SI units. A set of FPC compatible with this criterion is considered.
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