The aim of this work is to clarify the mathematical models describing the mechanics of rarefied gas and continuous mechanics, and to study the errors that arise when describing a rarefied gas by the framework of a continuous medium through the distribution function. We also trace the errors of numerical calculations. In conservation laws for space coordinates, averaging is fulfilled but for times it is not. So we have laws that are not symmetric relative to time and space. It should be noted that for the kinetic theory (the Boltzmann equation), the law of conservation of angular momentum does not hold. However, writing conservation laws via delta functions, the same classical definition is obtained. Proposed analysis for derivative is to consider the difference between the time derivatives as a limit (the ratio of the increment of the function to the small increment of the argument). In a rarefied gas, we have end values of the mean free path and time. The results of the analysis show which effects are lost when the discrete medium is approximated by a distribution function. As an example of the solutions, a formula is given for calculating the distance of flow of a jet of gas at large non-calculative supersonic flow upstream.