The solution of the paradox „Dichotomy“ by means of the sum of the infinite geometrical order inconsequently considers the division towards the end point. In the paradox the beginning of the motion is made problematic by the consequent division towards the starting point. Moreover the solution breaks the mathematical model, it confuses the demarcation of the order by means of a limit with the attainment of a limit. Later the author formulates his opinion on the paradox from the standpoint of the dialectical-materialist conception of motion. The paradox reflects the contradiction between the potential infinity, comprehending the finite, partial levels which contain motion as something immanent, and the actual infinity as „causa sui“, excluding relatively the rise-extinction, i.e. change, motion. This contradiction is dialectical and is reflected by the notion of the real infinity as a connection, unity of the potential and actual infinity.