Abstract
The quantities of dimension one - known as the dimensionless quantities - are widely used in physics. However, the debate about some dimensionless units is still open. The paper brings new interrelated arguments that lead to the conclusion to avoid physical dimensionless units, except one for the mathematical multiplication identity element that should not be introduced into a system of physical units. It brings the coherence to the International System of Units (SI) and it will remove ambiguities rising from the conflict between the mathematical properties and the physical conventions.
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