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The quantities of dimension one - known as the dimensionless quantities - arewidely used in physics. However, the debate about some dimensionless units isstill open. The paper brings new interrelated arguments that lead to theconclusion to avoid physical dimensionless units, except one for themathematical multiplication identity element that should not be introduced intoa system of physical units. It brings the coherence to the International Systemof Units (SI) and it will remove ambiguities rising from the conflict betweenthe mathematical properties and the physical conventions.

Why dimensionless units should not be used in physics